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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.05
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908154
  j =  2                              :            45923
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907813
  j =  2                              :            46089
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17486.36
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.81
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.84
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.30
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.44
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.50
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.64
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:30.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5100.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999798845

Normal statistic for number of bits   :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.58
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000011044

Normal statistic for number of bits   :   0.087
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:09.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 622611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.37
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.03
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.52
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.29
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908021
  j =  2                              :            45982
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907820
  j =  2                              :            46087
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.02
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.48
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.27
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.22
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  301.51
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.17
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.91
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  257.20
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:30.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999827498

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.13
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000082801

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:35.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1212435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9970

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.50
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:54.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907836
  j =  2                              :            46076
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908529
  j =  2                              :            45728
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  8.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.94
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.62
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.56
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.75
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.01
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.65
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.64
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.38
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  5.1e-4    *****

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10417.98
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.02
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.49
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000018607

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.64
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999917648

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:06.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2228243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5261
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    3.91
p-value of test                       :  9.6e-3

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.23
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.91
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.05
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.24
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.14
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45618
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869618
  j =  1                              :        399908767
  j =  2                              :            45612
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908301
  j =  2                              :            45848
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17374.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.97
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.85
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.52
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.32
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3940.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.68
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999924020

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.14
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999973082

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9941

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:23.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3276819.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:56.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908241
  j =  2                              :            45872
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907910
  j =  2                              :            46042
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 4.02e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.36e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.67
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.38
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.34
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.23
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.98
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.94
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.52
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.30
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.95
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:35.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.82
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999833138

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.10
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000092374

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:42.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4456467.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:55.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908745
  j =  2                              :            45626
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46314
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870314
  j =  1                              :        399907375
  j =  2                              :            46308
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    : 1.21e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9986


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.96e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.40
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.30
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.30
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.56
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.16
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.24
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.53
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.91
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.55
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.32
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.97e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:31.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4303.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000105505

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.79
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999907796

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.21
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:37.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5570579.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.73
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.51
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.25
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.70
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907805
  j =  2                              :            46090
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908102
  j =  2                              :            45946
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 9.22e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9983


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.56
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.01
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.43
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.92
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.82
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.29
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.83
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.28
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.83
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.54
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000007201

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.04
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999994400

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:42.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6455315.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.58
p-value of test                       :  6.0e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1320.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:31.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.44
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908394
  j =  2                              :            45794
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907945
  j =  2                              :            46026
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.90
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.99
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.36
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.78
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -401.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.62
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.35
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.53
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4298.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.62
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000006283

Normal statistic for number of bits   :   0.050
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.28
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999882167

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP, t = 16          6.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7307283.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.19
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5305.91
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908195
  j =  2                              :            45895
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.75e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -1.62e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.02
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17187.12
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.26
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.50
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.14
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  443.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.71
p-value of test                       :  6.1e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:31.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11515.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.23
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999836333

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.26
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999996617

Normal statistic for number of bits   :  -0.027
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.45
p-value of test                       :    0.9928

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:12.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8323091.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.01
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:32.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.98
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.28
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908057
  j =  2                              :            45967
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908199
  j =  2                              :            45899
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.42
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.82
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.88
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.63
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.31
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.52
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.94
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.89
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.94
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.58
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.29
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   95.78
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
Total number of bits:  8000033136

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.43
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000061510

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:10.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 101  Run of bits, r = 0              4.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9273363.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5207.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:58.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908734
  j =  2                              :            45627
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908088
  j =  2                              :            45956
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17167.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.04
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.50
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.45
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.08
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.37
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.54
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:30.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12189.18
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.05
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000108808

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000036928

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.13
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.7e-3

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:49.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10321939.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.73
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.23
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908452
  j =  2                              :            45768
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908314
  j =  2                              :            45834
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.62e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17086.94
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.67
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.93
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.32
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.74
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.87
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:34.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.10
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999937070

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.22
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000000703

Normal statistic for number of bits   : 5.56e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9923

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:29.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11337747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    3.16
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.43
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.23
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:58.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908272
  j =  2                              :            45861
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908183
  j =  2                              :            45904
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.07
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.82
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.98
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.77
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.35
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.97
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.19
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.30
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9611.45
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:30.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   87.70
p-value of test                       :  2.5e-3


-----------------------------------------------
Total number of bits:  7999901595

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.49
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000009418

Normal statistic for number of bits   :   0.074
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:26.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12419091.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:30.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.51
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:58.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907766
  j =  2                              :            46114
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908733
  j =  2                              :            45626
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17639.25
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   98.87
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.07
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.75
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.10
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.46
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.67
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9685.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:30.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11588.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.85
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000048751

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.83
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999964400

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:02.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13434899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    4.30
p-value of test                       :  6.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.02
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.60
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907881
  j =  2                              :            46052
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908285
  j =  2                              :            45850
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.60
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.92
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.01
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.36
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.01
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.31
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.74
p-value of test                       :  8.4e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.16
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.97
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11538.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.19
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000018649

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.91
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999931058

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:15.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14450707.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    5.73
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9950

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.49
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.28
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.38
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:59.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46255
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870255
  j =  1                              :        399907497
  j =  2                              :            46241
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    6.32
p-value of test                       :  7.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  6.0e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.19e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.88
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.45
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.27
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.58
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.36
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.40
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.68
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.04
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:29.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.52
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000149959

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.23
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000054418

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:03.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  6.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15433747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5560
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9973

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.56
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.03
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.40
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908161
  j =  2                              :            45915
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907907
  j =  2                              :            46042
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.92e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:19.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.72
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17155.95
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.97
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.21
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.55
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.72
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.53
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.19
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.29
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.17
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999900923

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.37
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000027559

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:17.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16449555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7565
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.73
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908143
  j =  2                              :            45915
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908098
  j =  2                              :            45945
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17661.02
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  425.78
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.92
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.59
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  306.32
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.41
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4801.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.52
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10242.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.80
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000019681

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.49
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000032767

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:30.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17498131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6914.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.28
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908746
  j =  2                              :            45621
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908108
  j =  2                              :            45943
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17732.25
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.60
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.55
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.33
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4735.86
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.26
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.17
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.70
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.35
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999989897

Normal statistic for number of bits   :  -0.080
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.36
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999925127

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18513941.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4170
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.70
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.96
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908714
  j =  2                              :            45640
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908650
  j =  2                              :            45672
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  7.4e-4    *****

Anderson-Darling statistic = A2       :    4.79
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:18.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:12.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:12.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.74e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.85
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.52
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.76
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.05
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.66
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.80
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.46
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.37
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.68
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.95
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:25.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.52
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000067303

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.99
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999846479

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:22.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19529749.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1337.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.42
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46407
p-value of test                       :  7.0e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870407
  j =  1                              :        399907188
  j =  2                              :            46403
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908053
  j =  2                              :            45972
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.30e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.91
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.75
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.75
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.26
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.12
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.12
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.64
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999994346

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999989369

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:06.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 655380.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.96
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4825.38
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:46.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908249
  j =  2                              :            45871
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908136
  j =  2                              :            45929
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:15.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:15.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:28.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.53
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.38
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16875.17
p-value of test                       :    0.9987



-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.96
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   50.28
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  185.43
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.24
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.39
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.36
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.58
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.69
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4323.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12154.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.15
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999975443

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.76
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000000019

Normal statistic for number of bits   : 1.50e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:15.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1736724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.92
p-value of test                       :  9.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     531
p-value of test                       :    0.9978

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    3.89
p-value of test                       :  9.9e-3

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.08
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.65
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907482
  j =  2                              :            46256
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907619
  j =  2                              :            46186
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.20
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.09
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.38
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.61
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.60
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.13
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.01
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.48
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9697.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 3.33e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:35.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.93
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999973337

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.29
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000078763

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:16.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 84  Fourier3, r = 0                 0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2555924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7255.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.31
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:46.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908533
  j =  2                              :            45729
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908051
  j =  2                              :            45970
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.55
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.01
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.09
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.65
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 9.95e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:34.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.43
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999875366

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.56
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000013651

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:58.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3178516.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.55
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908715
  j =  2                              :            45635
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908058
  j =  2                              :            45968
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:28.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.65
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.32
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.48
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.35
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.86
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.15
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.70
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999975347

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.50
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000050140

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:29.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4292637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6870.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.43
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.96
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:48.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908094
  j =  2                              :            45950
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908728
  j =  2                              :            45630
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9969


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:28.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17266.83
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.64
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.23
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.01
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.94
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.24
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.45
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.35
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.98
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:31.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.05
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000059578

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.70
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999985268

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:29.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5406749.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:39.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  103.87
p-value of test                       :  3.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.17
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907684
  j =  2                              :            46155
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908632
  j =  2                              :            45675
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 5.17e-4
p-value of test                       :  2.3e-5    *****

Anderson-Darling statistic = A2       :    5.75
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.76
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.63
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.72
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.99
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.63
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.95
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.15
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.00
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999897365

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.61
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999925730

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:28.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     3.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6422557.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:36.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.85
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.49
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908087
  j =  2                              :            45955
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908715
  j =  2                              :            45638
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.66
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.02
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.89
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.51
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.57
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.47
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.76
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.66
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.83
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.63
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:31.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.96
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999875579

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.60
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999984632

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:32.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7536669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9915

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.78
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.21
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.17
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:53.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46319
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870319
  j =  1                              :        399907368
  j =  2                              :            46307
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45487
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869487
  j =  1                              :        399909031
  j =  2                              :            45477
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.16e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.43
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17169.76
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.69
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.36
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.15
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.76
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:31.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.53
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.12
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999972422

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.44
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000081271

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.015
p-value of test                       :    0.51

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:24.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8290333.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5289
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.94
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908717
  j =  2                              :            45634
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908004
  j =  2                              :            45995
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.10
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.45
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.05
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.69
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.28
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.89
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.29
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.37
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  258.86
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.51
p-value of test                       :    0.9940

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.80
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.70
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:30.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11564.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.46
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999874325

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.36
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999955376

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:00.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9240605.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:37.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.34
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.93
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.73
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908548
  j =  2                              :            45714
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908437
  j =  2                              :            45774
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.79
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.27
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.94
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.17
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.12
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.01
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.20
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.22
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.47
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000026401

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.75
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000079036

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  6.9e-3

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:57.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10256413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     667
p-value of test                       :  3.8e-3

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.15
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45577
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869577
  j =  1                              :        399908847
  j =  2                              :            45575
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908161
  j =  2                              :            45912
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.60
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.28
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.53
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.50
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.85
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.35
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:29.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12106.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.03
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000028888

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.17
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000036451

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:48.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11304989.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1495
p-value of test                       :  2.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334615
  j =  1                              :        599997010
  j =  2                              :             1495
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7070
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.52
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.85
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907825
  j =  2                              :            46080
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17675.95
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.87
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.29
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.17
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.81
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4735.87
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.41
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.39
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.44
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.37e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9622.85
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:33.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5003.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12184.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.13
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999902456

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.69
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000186595

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:00.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            2.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12320797.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:37.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.01
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4739.96
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907967
  j =  2                              :            46009
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907788
  j =  2                              :            46103
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.76
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.65
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.28
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.78
p-value of test                       :  3.0e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.61
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.91
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:30.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.39
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.84
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999979430

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.55
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999848597

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:08.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13303837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5269
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7095
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:02:35.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     665
p-value of test                       :  4.7e-3

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.52
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.14
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908077
  j =  2                              :            45954
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908090
  j =  2                              :            45952
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.59
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.95
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.93
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.86
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9671.12
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:25.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.18
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999998717

Normal statistic for number of bits   :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.14
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999956147

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:13.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14352413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.55
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908437
  j =  2                              :            45777
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908235
  j =  2                              :            45878
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.77
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.75
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.16
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.61
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.44
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.37
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.10
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 7.21e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:29.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.89
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.02
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999932801

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.28
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000039958

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:04.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15368221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    5.66
p-value of test                       :  1.4e-3

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.96
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.92
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.22
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:58.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908304
  j =  2                              :            45845
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908112
  j =  2                              :            45938
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.93
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4780.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.20
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.16
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.51
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.57
p-value of test                       :    0.9900


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.71
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.07
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.89
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999922622

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.76
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999874919

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    2.49
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:38.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16384029.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.22
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908692
  j =  2                              :            45651
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908519
  j =  2                              :            45730
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9932


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:12.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17690.78
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.20
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.88
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.79
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.75
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.34
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10298.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.34
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000010582

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.30
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000045124

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:17.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17432605.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.34
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6792.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.34
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.35
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908380
  j =  2                              :            45807
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908375
  j =  2                              :            45811
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9906


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:19.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   34.89
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:30.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.17
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.06
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.67
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  201.96
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.46
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.46
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.06
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.44
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.60
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.75
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:24.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.54
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000034966

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.36
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999980846

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:20.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18448413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    3.59
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.78
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908017
  j =  2                              :            45987
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45414
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869414
  j =  1                              :        399909175
  j =  2                              :            45408
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:12.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -4.31e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17349.38
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.92
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.63
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.78
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.73
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.01
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:25.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.79
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.39
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999957251

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.40
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999930356

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19464221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.77
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:37.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.54
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.23
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907939
  j =  2                              :            46026
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908397
  j =  2                              :            45800
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17202.17
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.10
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.41
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.74
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.95
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.34
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4804.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  459.61
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.88
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.80
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -6.20e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:30.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.56
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000001690

Normal statistic for number of bits   :   0.013
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.02
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000051817

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:24.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 688149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7097
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.78
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    5.08
p-value of test                       :  2.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     530
p-value of test                       :    0.9981

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  500.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7284.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.51
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:29.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.07
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908044
  j =  2                              :            45969
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:28.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   69.50
p-value of test                       :  9.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.03
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.90
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.78
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.85
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.11
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  475.44
p-value of test                       :  9.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.77
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.10
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.95
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.42
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.48
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.53e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.62
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.90
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.04
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000211060

Normal statistic for number of bits   :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.47
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999846545

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.41

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    1.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:01.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 63  WeightDistrib, r = 10           9.6e-4
 78  RandomWalk1 M (L=10000, r=0)    9.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1277964.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1230
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334350
  j =  1                              :        599997540
  j =  2                              :             1230
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    3.65
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    3.57
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.42
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908295
  j =  2                              :            45851
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907994
  j =  2                              :            46000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:28.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.53
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.98
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.33
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.87
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.51
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4743.95
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.24
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.93
p-value of test                       :  7.9e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.81
p-value of test                       :    0.9976

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.74
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10299.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.41
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999980531

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.54
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999980498

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Tests on the sum of all N observations
Standardized normal statistic         : 1.62e-3
p-value of test                       :    0.50

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:39.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2949132.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.24
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.13
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.74
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.15
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908167
  j =  2                              :            45909
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908089
  j =  2                              :            45945
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:09.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17615.42
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.13
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.15
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.91
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.12
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4803.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.02
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.19
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9764.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11519.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.47
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999904586

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000152203

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:45.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3932172.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.48
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6844.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908209
  j =  2                              :            45894
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46249
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870249
  j =  1                              :        399907505
  j =  2                              :            46243
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.07
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.02
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.95
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.83
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  443.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.15
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.04
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.59
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.16
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.78
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999954689

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.78
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999869585

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:27.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4915212.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.69
p-value of test                       :  4.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6814.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   82.88
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.27
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907882
  j =  2                              :            46053
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45486
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869486
  j =  1                              :        399909032
  j =  2                              :            45478
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.21
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.93
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.86
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.62
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.17
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.37
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.57
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.95
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999895232

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.85
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000042730

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:31.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5865484.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.08
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.07
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.65
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.77
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907723
  j =  2                              :            46134
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45306
p-value of test                       :    0.9963


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869306
  j =  1                              :        399909391
  j =  2                              :            45300
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9907


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -7.56e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.74
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.88
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.04
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.49
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.96
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.20
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.42
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10394.96
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.23
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.30
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999877010

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.72
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000058000

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:24.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6881292.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5230
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.85
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4907.66
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908559
  j =  2                              :            45710
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.46
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.07
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.43
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.93
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.91
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.18
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.49
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.01
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.52
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.83
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000127264

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.14
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999963521

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.81

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:40.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7897100.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4490
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.75
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    3.56
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     810
p-value of test                       :    0.9988

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    3.31
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.54
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908695
  j =  2                              :            45651
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907917
  j =  2                              :            46037
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.74
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.88
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.05
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.50
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.68
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.60
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10279.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.69
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000008887

Normal statistic for number of bits   :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.24
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999871151

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:04.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8912898.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1489
p-value of test                       :  4.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334609
  j =  1                              :        599997022
  j =  2                              :             1489
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.96
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    3.77
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.26
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.85
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46181
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870181
  j =  1                              :        399907639
  j =  2                              :            46179
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908121
  j =  2                              :            45926
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.30
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.60
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.11
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.85
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.62
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.51
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.71
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.46
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.64
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000026383

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.88
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999983594

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.33
p-value of test                       :    0.01

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:46.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            4.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9830402.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9912


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.15
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909080
  j =  2                              :            45454
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907966
  j =  2                              :            46011
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.49
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.27
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.97
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.08
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.51
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.02
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.17
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.03
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.62
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.18
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  454.68
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.95
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.80
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.56
p-value of test                       :  6.4e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.73
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9734.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.15
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.80
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.08
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000025396

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000070432

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:46.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10911746.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    3.01
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.51
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46220
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870220
  j =  1                              :        399907563
  j =  2                              :            46214
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907649
  j =  2                              :            46168
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.89
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.14
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.91
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.40
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.53
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.32
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.33
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.94
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 4.81e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:36.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.69
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000082009

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.13
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999994043

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:33.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11829250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    7.15
p-value of test                       :  2.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9938


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  510.02
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.47
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908501
  j =  2                              :            45748
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908471
  j =  2                              :            45760
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.33
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17597.94
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.76
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.25
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.88
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.86
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.32
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.14
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11519.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12212.93
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.02
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000050200

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999882800

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         2.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12812290.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7113
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7526
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.96
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.53
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.67
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:29.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.18
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907818
  j =  2                              :            46082
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45586
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869586
  j =  1                              :        399908831
  j =  2                              :            45580
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  3.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.89e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.95
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.57
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.03
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.37
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.42
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.44
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.15
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10356.42
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 2.18e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4328.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.04
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000064855

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.91
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000265072

Normal statistic for number of bits   :    2.10
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:39.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13860866.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4502
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7103
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.96
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.90
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.49
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4841.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:03:00.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908484
  j =  2                              :            45752
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908055
  j =  2                              :            45962
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.42
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.27
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.49
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.93
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.19
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.93
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.41
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.61
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999849623

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.91
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000035314

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:00.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14942210.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    6.38
p-value of test                       :  6.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.64
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.45
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907703
  j =  2                              :            46144
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46493
p-value of test                       :  2.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870493
  j =  1                              :        399907018
  j =  2                              :            46485
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.12
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.77
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.80
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.31
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.52
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.73
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.34
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.31
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.83
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000123580

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.06
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999952310

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:33.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         6.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15892482.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.45
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.87
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.79
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.75
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907981
  j =  2                              :            46005
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908892
  j =  2                              :            45551
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.37e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17170.57
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.32
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.89
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.28
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  449.58
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.02
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.46
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.20
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000041476

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000033466

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:23.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16842754.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5226
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9969

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.69
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908714
  j =  2                              :            45637
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908745
  j =  2                              :            45623
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.87e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.095
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17607.37
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.22
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.03
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.88
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.51
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.22
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.35
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.83
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.87
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.53
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:03:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5084.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.21
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999974135

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.01
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000013900

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:30.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17989634.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.79
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.13
p-value of test                       :  2.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  497.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.01
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.87
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45567
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869567
  j =  1                              :        399908870
  j =  2                              :            45559
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908402
  j =  2                              :            45799
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 4.17e-4
p-value of test                       :  9.5e-4    *****

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.094
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17814.43
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   40.72
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.47
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.88
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.16
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5196.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.04
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.88
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.49
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.01
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3912.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.85
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000057040

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999988430

Normal statistic for number of bits   :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:56.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18874370.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.87
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1583.86
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.45
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907933
  j =  2                              :            46029
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17561.12
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.80
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.79
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.68
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.91
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.78
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.13
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.91
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:23.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.92
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.22
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000032653

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.99
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999900131

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:44.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19857410.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7126
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     537
p-value of test                       :    0.9952

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.39
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:57.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46380
p-value of test                       :  9.9e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870380
  j =  1                              :        399907241
  j =  2                              :            46378
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.46
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.02
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.55
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.12
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.69
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.77
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5076.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.85
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000081397

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.53
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999944189

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:14.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 720918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.81
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     818
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.14
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.68
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.86
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.76
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.80
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:54.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908277
  j =  2                              :            45857
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:27.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.70
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.79
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.35
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.11
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.91
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.23
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.28
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.03
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.70
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -401.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.17
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:31.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.49
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000138970

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.27
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000045727

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:56.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1802262.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.34
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.61
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.04
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908194
  j =  2                              :            45894
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46229
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870229
  j =  1                              :        399907544
  j =  2                              :            46225
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.57
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.96
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:27.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.13
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17852.45
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.44
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.13
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.12
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9942

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.00
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.73
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.29
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999885197

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.16
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000036454

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.091
p-value of test                       :    0.54

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:56.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2424854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.75
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.61
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.82
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5297.93
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:57.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908270
  j =  2                              :            45859
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.11
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.58
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  100.82
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.28
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.25
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.41
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.96
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.05
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.08
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.39
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.62
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999948557

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.38
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000023422

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:02.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3375126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.00
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.23
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908462
  j =  2                              :            45769
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46079
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870079
  j =  1                              :        399907845
  j =  2                              :            46073
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.42
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.02
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   14.16
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.30
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.93
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.66
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.31
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.32
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.68
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.39
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.29
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.62
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.70
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000024514

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000072850

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:47.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 M (L=50, r=25)      0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4751382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:38.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.02
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908385
  j =  2                              :            45806
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45607
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869607
  j =  1                              :        399908788
  j =  2                              :            45603
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.52
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.22
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.18
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.42
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.09
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.06
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.10
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.01
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.29
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10267.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5122.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.49
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000043180

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.94
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000067594

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:52.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5603350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.36
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907826
  j =  2                              :            46078
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46354
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870354
  j =  1                              :        399907294
  j =  2                              :            46350
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:28.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   57.01
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.26
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.80
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.64
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.89
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.42
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.34
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.65
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.49
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.00
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000173407

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.00
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999980555

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:26.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6488086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7538
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.97
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.37
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:53.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908045
  j =  2                              :            45973
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908294
  j =  2                              :            45844
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17030.58
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.48
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.43
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.99
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.16
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.60
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.87
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.96
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:36.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5080.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5111.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.55
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000107632

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.48
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999925205

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7733270.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.93
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    4.75
p-value of test                       :  3.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6787.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4869.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45552
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869552
  j =  1                              :        399908902
  j =  2                              :            45540
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46175
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870175
  j =  1                              :        399907657
  j =  2                              :            46161
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.60
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.67
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.31
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.12
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.85
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.68
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999895709

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.82
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999866495

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:25.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8716310.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1365.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:29.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.22
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.75
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908499
  j =  2                              :            45749
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908595
  j =  2                              :            45701
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:28.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.97
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.13
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.34
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.41
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.20
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.03
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999944894

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.95
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000048040

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9928726.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.69
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.85
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:54.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907814
  j =  2                              :            46090
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908071
  j =  2                              :            45963
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:15.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.02e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.09
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17042.70
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.49
p-value of test                       :    0.9928


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   94.41
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.42
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.92
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.36
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.95
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9696.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:21.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.32
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999892412

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.13
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999964397

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:40.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10944534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4182
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.23
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908781
  j =  2                              :            45605
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45573
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869573
  j =  1                              :        399908857
  j =  2                              :            45567
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:09.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17218.51
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.20
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.10
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.03
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.93
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   26.44
p-value of test                       :  8.8e-4    *****

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.12
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.49
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999791141

Normal statistic for number of bits   :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.01
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999928247

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:05.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 86  LongestHeadRun, r = 0           8.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11993110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  506.33
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7279.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908418
  j =  2                              :            45785
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908072
  j =  2                              :            45964
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17625.69
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.46
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.63
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.36
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.40
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.99
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.91
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10280.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4351.12
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.30
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999911063

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.38
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999959567

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.80
p-value of test                       :  3.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.75
p-value of test                       :    0.9970

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:00.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12976150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5285
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7083
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.86
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.26
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908354
  j =  2                              :            45817
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.37
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.78
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.71
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.72
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.35
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.54
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.62
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9674.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.35
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.19
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000000139

Normal statistic for number of bits   : 1.10e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.40
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000099589

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:41.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13991958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.27
p-value of test                       :  2.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    7.11
p-value of test                       :  3.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:46.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.38
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908187
  j =  2                              :            45896
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908445
  j =  2                              :            45773
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.70e-6
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.24
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.87
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.40
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.10
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.72
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.52
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.68
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.62
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.20
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.85
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.21
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999846851

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.62
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000106894

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.03

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:27.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         3.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14974998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9906


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.70
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.92
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.58
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.89
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908598
  j =  2                              :            45692
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908177
  j =  2                              :            45910
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.63
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.12
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.79
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.94
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.61
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.27
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.76
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.35
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.75
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.17
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999990488

Normal statistic for number of bits   :  -0.075
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.58
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000044788

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:07.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15958038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.64
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.21
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45501
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869501
  j =  1                              :        399909000
  j =  2                              :            45497
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908571
  j =  2                              :            45707
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.45
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.31
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.96
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   93.03
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.80
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.96
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.61
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.94
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999856697

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   87.26
p-value of test                       :  2.8e-3


-----------------------------------------------
Total number of bits:  8000361189

Normal statistic for number of bits   :    2.86
p-value of test                       :  2.1e-3



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:03.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16908301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.51
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.92
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.10
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908093
  j =  2                              :            45949
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908414
  j =  2                              :            45790
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17174.41
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.49
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.02
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.21
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.72
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.06
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4768.04
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4795.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.29
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12021.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000217180

Normal statistic for number of bits   :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.01
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999910847

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:33.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17858573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     975
p-value of test                       :  7.0e-3

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9938

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.34
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.61
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908672
  j =  2                              :            45658
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907929
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
p-value of test                       : 1 -  3.5e-5    *****

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.73
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.05
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.82
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.81
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.17
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.26
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.78
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.54
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.88
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.68
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999990788

Normal statistic for number of bits   :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.31
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999854444

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:02.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18776077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9985

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.41
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.22
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.58
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908166
  j =  2                              :            45911
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908562
  j =  2                              :            45710
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:19.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17627.71
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.30
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.91
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.97
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.91
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.01
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.59
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.38
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.21
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.01
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.35
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:29.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.44
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000020464

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.72
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999915056

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:53.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19726349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.95
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.44
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908319
  j =  2                              :            45839
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907797
  j =  2                              :            46097
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:28.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.13
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.97
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.36
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.02
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5286.36
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.17
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.03
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.80
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.06
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.38e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    4.98
p-value of test                       :  3.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  141.52
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.89
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000161410

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.37
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999931628

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    5.79
p-value of test                       :  1.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.18
p-value of test                       :  7.5e-4    *****

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:34.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 89  PeriodsInStrings, r = 20        0.9994 
 105  AutoCor, d=1, r=27              7.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 753687.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9907


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.95
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908204
  j =  2                              :            45895
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908525
  j =  2                              :            45727
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.20e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17181.95
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.25
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.11
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.89
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4337.57
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.65
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999985256

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.68
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000062599

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:23.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1441815.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   44.97
p-value of test                       :  4.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.39
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.59
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908096
  j =  2                              :            45949
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908404
  j =  2                              :            45789
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.13e-5
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.26
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.62
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.31
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:31.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4687.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.31
p-value of test                       :  9.5e-3


-----------------------------------------------
Total number of bits:  7999753110

Normal statistic for number of bits   :   -1.95
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.38
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999787004

Normal statistic for number of bits   :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:56.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               4.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2818071.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4500
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:36.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7282.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:26.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907900
  j =  2                              :            46047
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908256
  j =  2                              :            45866
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.32
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.53
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  601.60
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.88
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.13
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.89
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9770.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:35.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.21
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999960563

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000022057

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:55.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3637271.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9911

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.65
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6887.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.09
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:56.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908329
  j =  2                              :            45828
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908518
  j =  2                              :            45735
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.46
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17140.69
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.53
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.66
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.45
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.08
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.46
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.45
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000121954

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.50
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000062524

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:04.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4718615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.71
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908878
  j =  2                              :            45558
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908607
  j =  2                              :            45689
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.79e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.75
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.48
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.56
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.77
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.43
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.72
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.04
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999918950

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.33
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999979313

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:30.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5799941.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4496
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.98
p-value of test                       :  3.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.56
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.92
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908206
  j =  2                              :            45891
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46443
p-value of test                       :  4.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870443
  j =  1                              :        399907119
  j =  2                              :            46433
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16959.56
p-value of test                       :    0.9944



-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.90
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.29
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.36
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.32
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.31
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.07
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.05
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9758.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.53
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000079129

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.31
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000037213

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:52.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6815749.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997293
  j =  2                              :             1352
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:11.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.21
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.87
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.18
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.97
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908291
  j =  2                              :            45850
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908254
  j =  2                              :            45864
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17653.29
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.10
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.80
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.95
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.10
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.24
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.47
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.37
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3929.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.33
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999970532

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.06
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000077437

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.10
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7864325.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9966

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.84
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908595
  j =  2                              :            45698
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907698
  j =  2                              :            46142
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.29
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.91
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.13
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.15
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.35
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.89
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.37
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.69
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.43
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000082345

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.04
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000002197

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.25e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9909

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:02.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8847365.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    4.29
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.92
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:55.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908659
  j =  2                              :            45666
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908886
  j =  2                              :            45554
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.83
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.69
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.00
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.37
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.93
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.38
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.76
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.23
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5231.97
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.07
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.84
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.48
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.82
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.55
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999956423

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.34
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000096622

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:03.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9764869.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:47.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.36
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:59.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907900
  j =  2                              :            46047
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907979
  j =  2                              :            46006
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.12e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.91
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.08
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.65
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.24
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.47
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5223.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.48
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.39
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.34
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.42
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12049.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000020827

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.81
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000015559

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:03.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10878981.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.50
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.69
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.76
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908360
  j =  2                              :            45814
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907973
  j =  2                              :            46012
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17094.16
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.64
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.69
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.34
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.44
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.46
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.51
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000053893

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.44
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000043936

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:40.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11927557.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.97
p-value of test                       :  9.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.62
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4851.55
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:52.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907901
  j =  2                              :            46045
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908276
  j =  2                              :            45856
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.87e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.42
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.96
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.37
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.42
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4830.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.70
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4347.16
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12080.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.30
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999906602

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.68
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000089809

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12845061.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5305
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9941

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.84
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    3.67
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.35
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.99
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.54
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908561
  j =  2                              :            45715
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908284
  j =  2                              :            45852
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9967


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -3.12
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.06
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.78
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.00
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.68
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.73
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.44
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  184.82
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.86
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.28
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.14
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.09
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.90
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999980672

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.05
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999991370

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:18.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 57  AppearanceSpacings, r = 0       0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13959173.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    4.07
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9922

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:46.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.29
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.41
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399908995
  j =  2                              :            45501
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907924
  j =  2                              :            46032
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.46e-5
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.32
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.00
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.26
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.76
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.56
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10220.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.26
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000008422

Normal statistic for number of bits   :   0.067
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.54
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000013825

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:07.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15138821.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:47.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   18.73
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.20
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908329
  j =  2                              :            45828
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907957
  j =  2                              :            46020
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.62
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.71
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.10
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.03
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.51
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.12
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11556.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.54
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999937712

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.77
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999893474

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:58.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16154629.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4833.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907772
  j =  2                              :            46108
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908697
  j =  2                              :            45641
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.57
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17116.41
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.16
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.55
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.40
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.93
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.46
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.07e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.16
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000018196

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.30
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999843392

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:01.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17137669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.30
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.70
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908594
  j =  2                              :            45697
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908436
  j =  2                              :            45776
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.49
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.86
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.89
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    3.82
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.39
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.39
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.69
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.09
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.83
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.08
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.00
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.40
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.28
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.02
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10276.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:31.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3906.36
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.03
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999903722

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.51
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000060199

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:12.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 C (L=50, r=0)       0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18120709.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9982


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    3.54
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     541
p-value of test                       :    0.9923

Stat. AD (mNP2)                       :    2.45
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:29.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.20
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.00
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908441
  j =  2                              :            45769
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907773
  j =  2                              :            46109
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-6
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17224.04
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.99
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.77
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.15
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.29
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.50
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.75
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.33
p-value of test                       :    0.01

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.68
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999893015

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.91
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999905279

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:57.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19169285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4487
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    5.56
p-value of test                       :  1.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     536
p-value of test                       :    0.9958

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:29.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908316
  j =  2                              :            45830
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907836
  j =  2                              :            46073
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.37e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.42
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.72
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.31
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.35
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.11
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.84
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.03
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:28.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12084.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.67
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999956978

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.15
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000082423

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:40.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20185093.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9996    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  365.33
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1523.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7253.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.03
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.33
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908201
  j =  2                              :            45895
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908770
  j =  2                              :            45612
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.68e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.41
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.04
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.41
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.44
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.67
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:30.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.78
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999885737

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.03
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999959168

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.10
p-value of test                       : 1 -  3.7e-5    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:43.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 786456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    3.95
p-value of test                       :  9.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.24
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907467
  j =  2                              :            46259
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45484
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869484
  j =  1                              :        399909032
  j =  2                              :            45484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.42
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.30
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.22
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.26
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.37
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000078307

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.92
p-value of test                       :  8.4e-3


-----------------------------------------------
Total number of bits:  8000052768

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:13.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1572888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9980

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.47
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.52
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908290
  j =  2                              :            45855
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908192
  j =  2                              :            45898
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:29.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.62
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.50
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.81
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.60
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.20
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.57
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.53
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.50
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.70
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.96
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.96
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999888650

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.22
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000100963

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.083
p-value of test                       :    0.47

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:16.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2359304.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5580
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4139
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    3.34
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.47
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.88
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.84
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:47.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907927
  j =  2                              :            46035
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908364
  j =  2                              :            45809
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.97
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.39
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.56
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.54
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.37
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.66
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.31
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.45
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.91
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9704.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:35.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5054.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12052.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.09
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  7999833327

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.75
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000015439

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:16.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3407880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997327
  j =  2                              :             1335
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5236
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.79
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:53.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908221
  j =  2                              :            45885
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908250
  j =  2                              :            45869
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17588.10
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.37
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.87
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.27
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.01
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.15
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.97
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.12
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999982868

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.59
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999975371

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:59.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4227080.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5263
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.43
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.76
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.08
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:47.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908394
  j =  2                              :            45797
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908533
  j =  2                              :            45732
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.52
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.98
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.13
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.70
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.57
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.77
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.75
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999965591

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.32
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999940520

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5242888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.15
p-value of test                       :    0.9983

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.97
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.56
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46160
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870160
  j =  1                              :        399907684
  j =  2                              :            46152
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908469
  j =  2                              :            45761
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.29
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.10
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17609.75
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.34
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5311.38
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.05
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.42
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.71
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:31.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   91.01
p-value of test                       :  1.2e-3


-----------------------------------------------
Total number of bits:  7999872003

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999967634

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:45.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6193160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9970

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.26
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.24
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46230
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870230
  j =  1                              :        399907543
  j =  2                              :            46224
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908379
  j =  2                              :            45806
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:19.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.34
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.61
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.06
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  182.75
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.91
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.02
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.05
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.76
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.85e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9576.04
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:30.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.21
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999964385

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.80
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000076981

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7503880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:48.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.70
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7181.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.83
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907918
  j =  2                              :            46038
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907916
  j =  2                              :            46039
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.23e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  173.40
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.56
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.21
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.57
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  192.72
p-value of test                       :  1.0e-3    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.36
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.79
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -401.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.46
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:35.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.48
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000020569

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.09
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000130486

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:48.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    1.0e-3
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8257544.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.18
p-value of test                       :  7.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.43
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:32.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.00
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:53.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46239
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870239
  j =  1                              :        399907527
  j =  2                              :            46229
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46315
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870315
  j =  1                              :        399907373
  j =  2                              :            46309
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.74
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 1.27e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.64
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.82
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.72
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.49
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.61
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.32
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.48
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5106.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.78
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999937316

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.21
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999921470

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9306120.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9909

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:38.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  173.56
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.27
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.37
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908027
  j =  2                              :            45976
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:19.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.14
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.29
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.86
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.64
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.92
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.38
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.17
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.37
p-value of test                       :    0.9911

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.55
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-5
p-value of test                       : 1 -  1.4e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10393.59
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -5.31e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:30.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.79
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999911114

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.28
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999991406

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:04.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10289160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4183
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.29
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.16
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908126
  j =  2                              :            45931
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908704
  j =  2                              :            45645
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9923


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:19.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.34
p-value of test                       :  4.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17144.47
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.80
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.94
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.96
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.72
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000145048

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.30
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000048979

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:27.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               4.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11272200.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.11
p-value of test                       :  7.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    4.78
p-value of test                       :  3.7e-3

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.08
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907765
  j =  2                              :            46110
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907464
  j =  2                              :            46265
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:12.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.08
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.06
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.10
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.53
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.78
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.14
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.83
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.72
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.24
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.01
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999961769

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.86
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000025033

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Tests on the sum of all N observations
Standardized normal statistic         :  -0.096
p-value of test                       :    0.54

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:45.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12288008.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.28
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908551
  j =  2                              :            45720
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    6.62
p-value of test                       :  5.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:19.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.00
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17430.84
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.50
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.58
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.41
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.93
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.23
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5240.20
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.26
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.71
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.42
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.89
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000119680

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.92
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999933017

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.48

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:25.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               5.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13271048.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    3.47
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  184.71
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.71
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.78
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908128
  j =  2                              :            45927
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908572
  j =  2                              :            45711
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.83e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:19.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:19.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:12.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:29.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.028
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17644.97
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.43
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.93
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.62
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.38
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.53
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.13
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.28
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.49
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:23.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.53
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000017086

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.33
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999927167

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:26.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14286856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4507
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.71
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.26
p-value of test                       :  2.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.72
p-value of test                       :  4.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   98.91
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.03
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.99
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.28
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:57.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46185
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870185
  j =  1                              :        399907635
  j =  2                              :            46175
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908111
  j =  2                              :            45937
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.23
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:29.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:29.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.26
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.99
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.12
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.14
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   32.49
p-value of test                       :  1.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.27
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.08
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.56
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5186.47
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.02
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000027712

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.53
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000037012

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:56.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15302664.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5565
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7112
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:34.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.92
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.67
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.22
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:52.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908443
  j =  2                              :            45774
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907725
  j =  2                              :            46130
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:18.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.72
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.54
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.04
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.66
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.57
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.50
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.69
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.33
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.66
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:29.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.74
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000024055

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.95
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000007177

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:24.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16318472.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5543
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    3.68
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   20.24
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.44
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45617
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869617
  j =  1                              :        399908766
  j =  2                              :            45617
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908435
  j =  2                              :            45781
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.83
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.04
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.93
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.57
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5251.61
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.01
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.62
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.64
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.70
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:29.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.95
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999935240

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.50
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999897161

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:53.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17334280.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.76
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.64
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.22
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908079
  j =  2                              :            45956
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46283
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870283
  j =  1                              :        399907438
  j =  2                              :            46275
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.12e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17079.38
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.67
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.57
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.22
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.04
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -403.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.44
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.47
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999877571

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.69
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000139765

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:36.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18350088.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7051
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9982


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9978

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.42
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.73
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907972
  j =  2                              :            46011
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908525
  j =  2                              :            45733
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.41
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.82
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.35
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.11
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.32
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12170.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.57
p-value of test                       :  2.1e-3


-----------------------------------------------
Total number of bits:  8000100105

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.98
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999956936

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.06
p-value of test                       :  1.1e-3

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:45.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8         0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19365896.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    3.74
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.48
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  279.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.11
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.51
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.80
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908095
  j =  2                              :            45951
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908499
  j =  2                              :            45746
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:28.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.099
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.53
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.59
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.44
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.31
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.60
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.29
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.20
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.48
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999863648

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.35
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000089638

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:28.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 819225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.32
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.61
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.90
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908410
  j =  2                              :            45789
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908598
  j =  2                              :            45698
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.77
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.56
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.97
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.13
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.13
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.47
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.61
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.14
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:30.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.89
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999901655

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.96
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999892796

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         : -1.70e-3
p-value of test                       :    0.50

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1409049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:28.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.02
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.06
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5304.98
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908115
  j =  2                              :            45938
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908070
  j =  2                              :            45962
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.83
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.29
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.12
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.45
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:47.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       : 1 -  9.0e-5    *****

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.64
p-value of test                       :    0.9958

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.06
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.16
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999968399

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000046906

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:01.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2195481.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     975
p-value of test                       :  7.0e-3

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.95
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908778
  j =  2                              :            45605
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907922
  j =  2                              :            46033
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.90e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:14.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.59
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.39
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.53
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.34
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  581.43
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.95
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.62
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.42
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.10
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.95
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.85
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.55
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:52.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5086.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.41
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000076237

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.22
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999857813

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:58.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4030489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.41
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.15
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:06.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907929
  j =  2                              :            46028
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908462
  j =  2                              :            45763
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.80e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17667.65
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.40
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.43
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.04
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.51
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.50
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.40
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.21
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.52
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.40
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.32
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.96
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.60
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.42
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000046876

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.06
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000071542

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.090
p-value of test                       :    0.46

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:52.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5013529.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7547
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.73
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46236
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870236
  j =  1                              :        399907531
  j =  2                              :            46230
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907654
  j =  2                              :            46170
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:14.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.75
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   66.40
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.93
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.52
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.44
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.20
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.66
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.00
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000160057

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.29
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999872954

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.48
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:17.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6029337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.51
p-value of test                       :  5.0e-3

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.12
p-value of test                       :    0.9998    *****

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.69
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908642
  j =  2                              :            45670
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908037
  j =  2                              :            45977
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:13.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.90e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17740.23
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.95
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.66
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12232.11
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.54
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999969131

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999987863

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:42.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7012377.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:47.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.71
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    5.54
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   11.51
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.81
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.31
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46252
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870252
  j =  1                              :        399907498
  j =  2                              :            46248
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45272
p-value of test                       :    0.9977


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869272
  j =  1                              :        399909464
  j =  2                              :            45256
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:15.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:15.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.24
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.17
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.16
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.67
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.74
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.81
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:34.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.58
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999979115

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999986675

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 38  Run, r = 0                      0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8028185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9923

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.57
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.44
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.92
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.24
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907748
  j =  2                              :            46123
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45395
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869395
  j =  1                              :        399909212
  j =  2                              :            45391
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17570.40
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.04
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.28
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.62
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.88
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.35
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.30
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9613.80
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:36.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  4.8e-4    *****

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  7.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5108.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.38
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.48
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999932288

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.28
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000086320

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8978457.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.13
p-value of test                       :    0.9995    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    4.53
p-value of test                       :  4.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.94
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.42
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908478
  j =  2                              :            45755
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908552
  j =  2                              :            45712
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17392.22
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.30
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.41
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.17
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.44
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.10
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.65
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.40
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -401.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.67
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11454.68
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.77
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999902843

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.64
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000006238

Normal statistic for number of bits   :   0.049
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.061
p-value of test                       :    0.52

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:15.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9961497.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9978

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.75
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.90
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907961
  j =  2                              :            46009
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908415
  j =  2                              :            45785
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17716.23
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.62
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4822.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.25
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10310.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4294.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.46
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999988769

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.42
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000091027

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:28.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11010073.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7574
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.39
p-value of test                       :  5.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.77
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.63
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908728
  j =  2                              :            45633
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907881
  j =  2                              :            46058
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.47
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.65
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.43
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.11
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999988379

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.54
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999930539

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:00.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11894809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7096
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  9.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    3.17
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:30.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.06
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907983
  j =  2                              :            46007
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908602
  j =  2                              :            45696
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.67
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.20
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.52
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.21
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.44
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.17
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.18
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.38
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10215.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.82
p-value of test                       :    0.9930


-----------------------------------------------
Total number of bits:  7999935465

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.48
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999942236

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  7.0e-3

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:12.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12877849.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    4.83
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.09
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.96
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.38
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908404
  j =  2                              :            45795
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45525
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869525
  j =  1                              :        399908951
  j =  2                              :            45523
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.41
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.92
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.62
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.11
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.98
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.80
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.16
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.61
p-value of test                       :    0.9907

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:31.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.99
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.89
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999852395

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.87
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999907826

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13828121.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.16
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9990    *****

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1336.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.35
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.57
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46314
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870314
  j =  1                              :        399907373
  j =  2                              :            46312
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908322
  j =  2                              :            45836
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.44e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.91
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.75
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.00
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  147.44
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.97
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10332.19
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4724.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.70
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999883235

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.38
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000184642

Normal statistic for number of bits   :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:29.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14811161.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.47
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:51.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908687
  j =  2                              :            45649
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908002
  j =  2                              :            45993
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17840.81
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.64
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   49.40
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.23
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.28
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.32
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.49
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.14
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.52
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.24
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10291.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.73
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999970850

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.04
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999995282

Normal statistic for number of bits   :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.95e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    5.30
p-value of test                       :  2.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.41
p-value of test                       :    0.9997    *****

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:15.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              1.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27              0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15794201.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    4.03
p-value of test                       :  8.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.91
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.55
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.26
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:55.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908592
  j =  2                              :            45701
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908539
  j =  2                              :            45729
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.44
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17069.63
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.46
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.77
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.14
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.64
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.97
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999848552

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.67
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000004942

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:43.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16810009.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4502
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     829
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:38.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7200.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.04
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.64
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907915
  j =  2                              :            46041
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45610
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869610
  j =  1                              :        399908783
  j =  2                              :            45604
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.03
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.59
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.75
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.39
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.55
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.41
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4300.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12264.30
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.95
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000122419

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.27
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000012304

Normal statistic for number of bits   :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:38.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17661977.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    4.01
p-value of test                       :  8.6e-3

Stat. AD after spacings (mNP2-S)      :    4.02
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    5.86
p-value of test                       :  1.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  505.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.45
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.78
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.51
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908339
  j =  2                              :            45829
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907759
  j =  2                              :            46116
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.36
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.32
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.92
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.84
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.03
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.87
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.38
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4659.26
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.38
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000057334

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.41
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999853346

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18612249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     839
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:52.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908496
  j =  2                              :            45749
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907696
  j =  2                              :            46146
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17157.23
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.27
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.05
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.09
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.74
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.38
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.68
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:28.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.31
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999922745

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.91
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000063337

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9922

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:20.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19693593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.09
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5268.25
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:57.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907898
  j =  2                              :            46045
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907661
  j =  2                              :            46165
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.73
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.68
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.62
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.82
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4795.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.91
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.85
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.50
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.81
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:32.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.09
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000030646

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.04
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999984722

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:17.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 851994.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7538
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.28
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908202
  j =  2                              :            45893
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.44e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:28.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.61
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17167.87
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.01
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.47
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.29
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.25
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.87
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.64
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.12
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.54
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12079.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.19
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999966749

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.15
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999807896

Normal statistic for number of bits   :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:57.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1966106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  9.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.35
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.89
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6863.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.75
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.29
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45522
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869522
  j =  1                              :        399908961
  j =  2                              :            45512
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908402
  j =  2                              :            45796
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.11e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.44
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.89
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.64
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.97
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.22
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.77
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.93
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.88
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.76
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000089524

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.33
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000125005

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:51.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2850842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.99
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.99
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.26
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45504
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869504
  j =  1                              :        399908998
  j =  2                              :            45492
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907721
  j =  2                              :            46135
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.82
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.98
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.75
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.83
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.28
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.19
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:31.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.24
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000046219

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000099289

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:16.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3801114.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1235
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334355
  j =  1                              :        599997530
  j =  2                              :             1235
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    3.33
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6827.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.99
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908177
  j =  2                              :            45910
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908467
  j =  2                              :            45759
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.58
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.63
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.26
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.67
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.28
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.49
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  484.78
p-value of test                       :  3.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.34
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11391.11
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.94
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999957758

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.79
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999883196

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:51.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 79  RandomWalk1 M (L=10000, r=15)   3.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4489242.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.51
p-value of test                       :  6.5e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.41
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908294
  j =  2                              :            45847
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45522
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869522
  j =  1                              :        399908959
  j =  2                              :            45516
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.42e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.09
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.35
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.00
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.90
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.77
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.09
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.44
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.91
p-value of test                       :  8.0e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.58
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:41.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4343.00
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4350.45
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.34
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.28
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000056338

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.08
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999911195

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:05.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           6.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5701658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7536
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.31
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:39.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.92
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1548.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.65
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.51
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.32
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908525
  j =  2                              :            45736
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907795
  j =  2                              :            46092
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.73
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.63
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.01
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.60
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.48
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.48
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.49
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.86
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    2.45
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9738.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:32.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3945.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4307.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.08
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000073918

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.37
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000045100

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    2.68
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6783002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9925

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7252.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.17
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.71
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907862
  j =  2                              :            46060
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45402
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869402
  j =  1                              :        399909196
  j =  2                              :            45402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.53
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.67
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.82
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.94
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.44
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.12
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.01
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.44
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.90
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000060505

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.34
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000056746

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.88e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:40.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7798810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.84
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.53
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907937
  j =  2                              :            46027
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45772
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869772
  j =  1                              :        399908461
  j =  2                              :            45762
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.48e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 3.19e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.71
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.52
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.20
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.98
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.02
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  213.88
p-value of test                       :  2.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.69
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.64
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.57
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000084439

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.23
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999935870

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.68
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:25.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 H (L=1000, r=20)    2.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8781850.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.86
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6876.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.52
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.64
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:55.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45391
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869391
  j =  1                              :        399909221
  j =  2                              :            45385
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908444
  j =  2                              :            45772
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.36e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.89
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.54
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.62
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.96
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.06
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.36e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:30.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.82
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000074437

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.43
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999838217

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9699354.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.74
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.64
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908329
  j =  2                              :            45831
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 4.69e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.03
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.81
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.79
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.94
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.80
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.84
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9782.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:30.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.33
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999912806

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.88
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000063940

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:53.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10485786.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     662
p-value of test                       :  6.6e-3

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.80
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.49
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908325
  j =  2                              :            45836
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908557
  j =  2                              :            45711
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17719.07
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.08
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.63
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.76
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.89
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.19
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.08
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.12
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.84
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.43
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.74
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.92
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.33
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.66
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.71
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000066241

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.39
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999963584

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11501594.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.57
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    6.10
p-value of test                       :  8.9e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1569.08
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6914.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.81
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.06
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4795.47
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908288
  j =  2                              :            45853
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908472
  j =  2                              :            45761
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-4
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.75
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17686.91
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.81
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.09
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.14
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.58
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.77
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -401.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:31.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4321.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.74
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999925286

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.20
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999888029

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.22
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.55
p-value of test                       :  5.3e-3

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:47.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          8.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12517402.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5537
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    3.41
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.65
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7248.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.57
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.03
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908531
  j =  2                              :            45733
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908377
  j =  2                              :            45807
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:15.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:15.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.77
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17784.58
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.35
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.90
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.76
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.78
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.99
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4668.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.77
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000070444

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999939389

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:34.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13795354.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9961

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:11.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4869.56
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908649
  j =  2                              :            45671
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.33
p-value of test                       :  4.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.14
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.68
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.20
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.26
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.09
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.09
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.44
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.96
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:31.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.27
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3910.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.14
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000005164

Normal statistic for number of bits   :   0.041
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.73
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000053260

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:49.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               4.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14778394.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.45
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.87
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.44
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4870.94
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:00.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908033
  j =  2                              :            45973
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907724
  j =  2                              :            46138
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.20
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.49
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.54
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.61
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4744.50
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.40
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.69
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.45
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.32
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.88
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  147.11
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10307.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.87
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000004546

Normal statistic for number of bits   :   0.036
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.01
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999990935

Normal statistic for number of bits   :  -0.072
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:53.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15597594.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7594
p-value of test                       :  6.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.97
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5256.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908331
  j =  2                              :            45833
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908128
  j =  2                              :            45933
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17202.19
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.92
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.88
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.12
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.23
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.58
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.17
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.41
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.32
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000035869

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.36
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999992054

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:43.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 15  BirthdaySpacings, t = 4         6.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16613402.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:28.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9945

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.23
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6874.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:30.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.46
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.83
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908836
  j =  2                              :            45582
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908461
  j =  2                              :            45768
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.02
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17704.02
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.97
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.17
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.80
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.81
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.64
p-value of test                       :  6.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.93
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.46
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 6.62e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3842.46
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.96
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999984797

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.34
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999992867

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:50.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17727514.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9994    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.02
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7208.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.18
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.85
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908024
  j =  2                              :            45985
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907980
  j =  2                              :            46007
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.80
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.68
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.84
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.76
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.84
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.80
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.64
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.02
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000159463

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.77
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000006841

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:00.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19071002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.54
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908618
  j =  2                              :            45685
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908483
  j =  2                              :            45757
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.34
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.47
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.31
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.87
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  311.05
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.06
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.34
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.50
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:23.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3886.64
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.56
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000054511

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.42
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000100849

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:49.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20086810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.89
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.74
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.35
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908455
  j =  2                              :            45771
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908174
  j =  2                              :            45907
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.04e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    5.13
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17175.10
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.89
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.51
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.35
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.77
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.76
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.27
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.83
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.34
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.4e-4    *****

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10388.20
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10225.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.22
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999945233

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.13
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999980657

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:22.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 884763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.09
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7237.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.73
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908263
  j =  2                              :            45864
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45360
p-value of test                       :    0.9924


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869360
  j =  1                              :        399909283
  j =  2                              :            45354
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:27.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.32
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.19
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.63
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.24
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.57
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.00
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.86
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:30.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11522.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.36
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999952742

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.56
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000134830

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.45
p-value of test                       :    0.9929

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:54.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1343515.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4173
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:37.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.78
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.00
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.92
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.95
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908308
  j =  2                              :            45837
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908290
  j =  2                              :            45852
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.06
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.20
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.15
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.81
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.68
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.25
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.92
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.56
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.22
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.38
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.20
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:30.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.95
p-value of test                       :  3.0e-3


-----------------------------------------------
Total number of bits:  7999883883

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.44
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999965540

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:16.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2129947.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1483
p-value of test                       :  7.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334603
  j =  1                              :        599997034
  j =  2                              :             1483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6803.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.48
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45386
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869386
  j =  1                              :        399909232
  j =  2                              :            45378
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45232
p-value of test                       :    0.9988


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869232
  j =  1                              :        399909538
  j =  2                              :            45228
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17869.61
p-value of test                       :  9.7e-3



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.99
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.39
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.78
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.23
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.49
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.32
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.46
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999987887

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.88
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000125989

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.20e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:48.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           7.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3571739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5252
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    4.84
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.25
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.13
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907953
  j =  2                              :            46019
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908012
  j =  2                              :            45988
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.05
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.29
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.18
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.56
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.75
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.01
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.74
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999968861

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000000271

Normal statistic for number of bits   : 2.14e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.99

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:35.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4522011.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9984

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.00
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.88
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.83
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.95
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908522
  j =  2                              :            45730
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908649
  j =  2                              :            45671
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9914


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.084
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.04
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.65
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.27
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.39
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.74
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.17
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:31.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.46
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999918041

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.84
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999870584

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:06.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5373979.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7055
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.40
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.39
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908311
  j =  2                              :            45840
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908490
  j =  2                              :            45749
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.51
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.14
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.17
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.98
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.36
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.47
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.00
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.38
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.15e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.83
p-value of test                       :    0.9977

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 4.67e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    6.92
p-value of test                       :  3.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4528.11
p-value of test                       : 1 -  9.0e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.79
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000045622

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.80
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999977759

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:18.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 96  HammingIndep, L=30, r=27       1 -  9.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6357019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.49
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    3.00
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   24.99
p-value of test                       :  7.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  518.15
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.32
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907908
  j =  2                              :            46037
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908696
  j =  2                              :            45649
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.89e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.25
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  3.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    7.58
p-value of test                       :  2.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.50
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.11
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.11
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.63
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.29
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.97
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.24
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.11
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.22
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.92
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.55
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4668.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5111.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4315.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.87
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000006427

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.89
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000006229

Normal statistic for number of bits   :   0.049
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:11.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               7.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7405595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.35
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.14
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.75
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.62
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:56.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908478
  j =  2                              :            45755
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908169
  j =  2                              :            45914
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.05e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.12
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.41
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.06
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   41.87
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.50
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.64
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.60
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4795.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.02
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.86
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.08
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.11
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9754.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.54
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.36
p-value of test                       :    0.9915


-----------------------------------------------
Total number of bits:  8000179137

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.50
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999985883

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.43
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.73e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.40
p-value of test                       :    0.9919

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:23.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8421403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:36.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6941.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.06
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.72
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:54.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45470
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869470
  j =  1                              :        399909061
  j =  2                              :            45468
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908176
  j =  2                              :            45909
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.00e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.33
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.37
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.85
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.31
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.97
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.84
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.22
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.55
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.50
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000069355

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.93
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999942794

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:38.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9404443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.20
p-value of test                       :  2.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     540
p-value of test                       :    0.9931

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.02
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.32
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7255.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.48
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.19
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.03
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45507
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869507
  j =  1                              :        399908991
  j =  2                              :            45497
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908168
  j =  2                              :            45910
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9969


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.45e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.05
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.25
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.55
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.93
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.13
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.24
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.46
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.09
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.86
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000058219

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.62
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999934058

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    2.61
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10453019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4154
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.65
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.22
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.10
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908620
  j =  2                              :            45687
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908612
  j =  2                              :            45688
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.80
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.45
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.45
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.58
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.23
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.23
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.12
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:30.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.69
p-value of test                       :  7.2e-3


-----------------------------------------------
Total number of bits:  7999928103

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.36
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000046252

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.41
p-value of test                       :  8.1e-3

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11534363.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     542
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.50
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.31
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.13
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908228
  j =  2                              :            45880
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908745
  j =  2                              :            45623
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.72
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.34
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.83
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.06
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.12
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.04
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.79
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.72
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.59
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.48
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000053203

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.02
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000147304

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12550171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7228.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907542
  j =  2                              :            46223
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908335
  j =  2                              :            45828
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.16
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.15
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.79
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5186.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.12
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.81
p-value of test                       :    0.9968


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:31.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12132.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.35
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999943100

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.12
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999902681

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:47.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13664283.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.94
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.21
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908329
  j =  2                              :            45834
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908266
  j =  2                              :            45864
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.79
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17729.77
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.76
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.01
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5222.58
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.89
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.95
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.45
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000062725

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.32
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000041407

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:39.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14614555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5556
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7088
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.73
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.22
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907782
  j =  2                              :            46100
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908408
  j =  2                              :            45790
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.05
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.20
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.86
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   94.63
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.12
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.32
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.59
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.76
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.45
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.37
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.64
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000060220

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000012625

Normal statistic for number of bits   :   0.100
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         : 7.98e-3
p-value of test                       :    0.50

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:05.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15663131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   39.15
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.36
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908123
  j =  2                              :            45928
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908476
  j =  2                              :            45756
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.21
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   44.30
p-value of test                       :  3.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.95
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.93
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.83
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.84
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.13
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:31.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.49
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.35
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999990056

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.40
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000037555

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.69
p-value of test                       :  3.5e-3

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    2.43
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:52.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 C (L=50, r=0)       3.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16744475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.18
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.16
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4866.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908672
  j =  2                              :            45658
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907733
  j =  2                              :            46129
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.08
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.29
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.59
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.96
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.15
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.38
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.02
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.87
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.27
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.49
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999894794

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.01
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999999758

Normal statistic for number of bits   : -1.91e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:43.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17760283.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.05
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.24
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:02:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908022
  j =  2                              :            45974
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908492
  j =  2                              :            45742
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.83
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.28
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.51
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.53
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.50
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.67
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -3.45e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:30.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.03
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999996767

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.98
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999924182

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:50.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18939931.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:36.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.42
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908270
  j =  2                              :            45859
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908148
  j =  2                              :            45917
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.73
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.84
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4769.43
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.55
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.18
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.38
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.77
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5091.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.71
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999956198

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.18
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999827312

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.51
p-value of test                       :    0.9939

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:36.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19890203.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4498
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9920


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:35.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.10
p-value of test                       :  8.3e-3


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:57.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908330
  j =  2                              :            45832
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45466
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869466
  j =  1                              :        399909072
  j =  2                              :            45458
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.71
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.89
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.27
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.49
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.96
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.42
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.95
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   31.22
p-value of test                       :  1.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -401.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.84
p-value of test                       :  2.3e-3

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.55
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999978629

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000001414

Normal statistic for number of bits   :   0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:38.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 917532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6777.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.81
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5236.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908449
  j =  2                              :            45771
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908532
  j =  2                              :            45725
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.39e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.18
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.88
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.68
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.09
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.01
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.50
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.74
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.82
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12228.06
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.28
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999988718

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.97
p-value of test                       :    0.9950


-----------------------------------------------
Total number of bits:  7999909047

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   0.047
p-value of test                       :    0.48

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:35.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1933340.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9980


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.26
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.98
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.85
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.38
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908175
  j =  2                              :            45911
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908771
  j =  2                              :            45613
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.77
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.44
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.78
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.90
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.66
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.21
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.80
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:31.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12092.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.02
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000062167

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.94
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999847889

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:46.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2883612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.36
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.25
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908713
  j =  2                              :            45636
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907862
  j =  2                              :            46057
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    6.17
p-value of test                       :  8.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9924


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17623.42
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.99
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.99
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.29
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.89
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  145.60
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.27
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.78
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9762.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:35.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.88
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000060760

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.16
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000004192

Normal statistic for number of bits   :   0.033
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.010
p-value of test                       :    0.50

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:39.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                8.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3768348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.24
p-value of test                       :  6.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1527.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.25
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46186
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870186
  j =  1                              :        399907631
  j =  2                              :            46180
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907860
  j =  2                              :            46067
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.81e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.06
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.42
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.66
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.51
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.45
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.70
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.67
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.74
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.16
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.71
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.46
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.79
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.00
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000065737

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.44
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000059410

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:49.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4947996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:46.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:27.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:28.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:40.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.19
p-value of test                       :  7.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.79
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:28.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.87
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:51.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907821
  j =  2                              :            46085
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.14
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.80
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.46
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.60
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.72
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.35
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.52
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.27
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.75
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.42
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.42
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.13
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:31.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.23
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999995192

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.34
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000055177

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:21.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5963804.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.47
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907859
  j =  2                              :            46066
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908990
  j =  2                              :            45502
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.83
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:29.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.72
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.16
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.54
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.20
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.49
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.76
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:30.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4300.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.34
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999997136

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.14
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999984476

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:54.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7077916.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9981

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  368.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6822.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.44
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:28.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.37
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908163
  j =  2                              :            45917
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907871
  j =  2                              :            46057
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.26e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.39
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.44
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.78
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.77
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.79
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.63
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  284.94
p-value of test                       : 1 -  4.5e-5    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.48
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.62
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.68
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999925760

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000075568

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Tests on the sum of all N observations
Standardized normal statistic         :   0.052
p-value of test                       :    0.48

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:50.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)  1 -  4.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8093724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:51.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.87
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.98
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908606
  j =  2                              :            45691
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908465
  j =  2                              :            45760
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.3e-3


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.41
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.32
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.19
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.54
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.87
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.37
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.90
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.39
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.75
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4356.60
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11462.21
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.97
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999890195

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.02
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999999986

Normal statistic for number of bits   : -1.11e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9109532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.24
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.34
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908096
  j =  2                              :            45946
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907860
  j =  2                              :            46067
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.34e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.53
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17249.70
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.47
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.19
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.81
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.19
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.32
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.30
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12106.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.92
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000155254

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.22
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000195820

Normal statistic for number of bits   :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:26.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10125340.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    4.67
p-value of test                       :  4.1e-3

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:47.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908191
  j =  2                              :            45903
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908064
  j =  2                              :            45965
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:27.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.59
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.40
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.56
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.17
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.74
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.43
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.73
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.79
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000120679

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.00
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999862325

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:21.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11141148.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7058
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.39
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.46
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.75
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46303
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870303
  j =  1                              :        399907399
  j =  2                              :            46293
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908258
  j =  2                              :            45868
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17554.05
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.27
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.66
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.39
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.04
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.61
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.79
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.08
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -403.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.43
p-value of test                       :    0.9938

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.17
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11533.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11529.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.61
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999972506

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.15
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000058333

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:23.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12091420.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4179
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.62
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.31
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46206
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870206
  j =  1                              :        399907589
  j =  2                              :            46204
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908516
  j =  2                              :            45733
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.31e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.97
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.78
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.64
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.86
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.88
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.84
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.62
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.11
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.89
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.97
p-value of test                       : 1 -  3.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.80
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.87
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999986153

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.60
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999959348

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.82
p-value of test                       :  2.4e-3

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:54.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 94  HammingCorr, L = 1200          1 -  3.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13107228.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.82
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.08
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:54.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908234
  j =  2                              :            45874
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45561
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869561
  j =  1                              :        399908880
  j =  2                              :            45557
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17687.86
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.23
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.71
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.09
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  481.44
p-value of test                       :  5.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.91
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.83
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.19
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.65
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.10
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.91
p-value of test                       :  3.0e-3


-----------------------------------------------
Total number of bits:  8000051151

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.06
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999956447

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.41
p-value of test                       :  8.0e-3

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:31.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 M (L=10000, r=0)    5.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14090268.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7094
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.15
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:47.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1336.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.52
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.78
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.66
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908168
  j =  2                              :            45916
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908092
  j =  2                              :            45951
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.96
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.66
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.02
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.35
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.31
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.58
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.25
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:35.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.51
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999873737

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.80
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000072346

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    2.43
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:45.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15171612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   91.36
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.19
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   35.28
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.94
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908041
  j =  2                              :            45975
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.42e-4
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.70
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.51
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.13
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.89
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.37
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.79
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.02
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.61
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4662.49
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.83
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000104836

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.93
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000014212

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:14.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16220188.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7527
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.98
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:49.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.59
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908509
  j =  2                              :            45738
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907572
  j =  2                              :            46205
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  1.0e-2


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.68
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.71
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.32
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.89
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.70
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.07
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.48
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000106507

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.17
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000053104

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:30.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17235996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9949

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.50
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.39
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.82
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:54.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45485
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869485
  j =  1                              :        399909032
  j =  2                              :            45481
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.99
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.05
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.05
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.73
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.71
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.28
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.68
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.55
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.35
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.77
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.20
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:31.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.38
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000035287

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.83
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000053836

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:32.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18219036.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5203
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:46.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.08
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.74
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:51.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908414
  j =  2                              :            45787
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908016
  j =  2                              :            45986
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.68e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.00
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.74
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.10
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.14
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.62
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.10
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.86
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.89
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:31.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.77
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999943493

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000105217

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:43.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19234844.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:28.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.64
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.43
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907834
  j =  2                              :            46077
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908388
  j =  2                              :            45806
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.65
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.14
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.82
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.04
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.56
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.17
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.58
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.66
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999958328

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.08
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999949481

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:42.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            5.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20250652.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:02:39.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.73
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6848.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.21
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908400
  j =  2                              :            45788
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908438
  j =  2                              :            45778
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.84
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.71
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.51
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.00
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.95
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.57
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.86
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.54
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -401.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.91
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.39
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999919292

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.71
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999936485

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:07.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 950301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5252
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     667
p-value of test                       :  3.8e-3

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.69
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.89
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.71
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:53.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908053
  j =  2                              :            45972
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908499
  j =  2                              :            45746
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17553.23
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.27
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.36
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.49
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.92
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.34
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.06
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.01
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.65
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.16
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.43
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10207.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:31.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4742.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.36
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999924794

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.58
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000049789

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    2.69
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:26.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1835017.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    5.55
p-value of test                       :  1.6e-3

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9910

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:39.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.85
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.40
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17116.39
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.62
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.89
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.27
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.50
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.68
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.94
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.08
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.31
p-value of test                       :  9.2e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10237.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:31.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.22
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999864026

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.17
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000148900

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:00.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2654217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.21
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.41
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908222
  j =  2                              :            45886
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:27.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.96
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.31
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.86
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.09
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.54
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.66
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:30.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.81
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.86
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000048133

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.65
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000040474

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:26.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3604489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.98
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.52
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907573
  j =  2                              :            46206
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46214
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870214
  j =  1                              :        399907574
  j =  2                              :            46210
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9939


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17218.54
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.64
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.88
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.72
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.39
p-value of test                       :  4.9e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.83
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  4.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.97
p-value of test                       :  3.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.74
p-value of test                       :    0.9970

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9780.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000050980

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.57
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999984422

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:19.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4161545.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.89
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.83
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907674
  j =  2                              :            46157
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908544
  j =  2                              :            45725
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.50e-5
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.75
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.99
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.42
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.23
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.62
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.43
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.13
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.76
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.69
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.27
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.63
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999953801

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999917468

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:22.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5144585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    4.86
p-value of test                       :  3.4e-3

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:33.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.21
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.77
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908143
  j =  2                              :            45918
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.83e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.52
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.51
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.30
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.10
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.19
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.35
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.07
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.08
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.15
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.66
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000089359

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.30
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999861806

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6160393.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:31.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:58.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:00.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:23.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.95
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.94
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:52.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908480
  j =  2                              :            45754
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907947
  j =  2                              :            46025
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.22e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.61
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.26
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17950.59
p-value of test                       :  2.9e-3



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.84
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.77
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.01
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.38
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.77
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.94
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.00
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.78
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.88
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12086.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.20
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000065797

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.41
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000005653

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:44.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7176201.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.62
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:28.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.97
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.84
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46185
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870185
  j =  1                              :        399907633
  j =  2                              :            46179
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.81e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17708.86
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.51
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.95
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.15
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.79
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.95
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.26
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.53e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.24
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.23
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000046156

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.25
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000223600

Normal statistic for number of bits   :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.18
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8617993.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.43
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.08
p-value of test                       :  2.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.19
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.14
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.45
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908318
  j =  2                              :            45841
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908346
  j =  2                              :            45824
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.87e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.98
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.52
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.31
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.56
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.63
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.35
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.36
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.62
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.97
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:30.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.48
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000087610

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.64
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000105499

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:57.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9437193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4505
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9930


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:40.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4830.95
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:54.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908617
  j =  2                              :            45684
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907928
  j =  2                              :            46030
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.39
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.91
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.74
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.21
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.85
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.26
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.41
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.84
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.96
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:30.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5115.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.56
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000044350

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.16
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000025534

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:01.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10354697.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.99
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.61
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908306
  j =  2                              :            45844
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907968
  j =  2                              :            46013
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.24
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.60
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.27
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.64
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.48
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.30
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.16
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.87
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.82
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.17
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.86
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10304.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.76
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999904835

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.55
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000030235

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    3.08
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:49.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11370505.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5566
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.34
p-value of test                       :  6.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.57
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.99
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907955
  j =  2                              :            46018
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46286
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870286
  j =  1                              :        399907430
  j =  2                              :            46282
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  102.59
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17667.79
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.32
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.53
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.50
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.30
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.21
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:29.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.71
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.74
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000013249

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.28
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000089443

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:04.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12353545.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.94
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1554.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.69
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.46
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908101
  j =  2                              :            45945
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908601
  j =  2                              :            45692
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.06e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.83
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.87
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.65
p-value of test                       :    0.9959

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.97
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:29.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.18
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999970745

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999974795

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:45.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13402121.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.30
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.43
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.33
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908316
  j =  2                              :            45836
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.06
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.91
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.40
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.19
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.89
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.59
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5221.97
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.51
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:17.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.83
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.00
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999915173

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.58
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000110230

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.070
p-value of test                       :    0.47

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:45.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14417929.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5291
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7248.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908232
  j =  2                              :            45878
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46241
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870241
  j =  1                              :        399907520
  j =  2                              :            46237
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.77
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.45
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.86
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  302.42
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.62
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.61
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.08
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.61
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:28.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.78
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000140356

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.92
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000019657

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15400969.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     971
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:39.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.08
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.36
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908398
  j =  2                              :            45795
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907896
  j =  2                              :            46049
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:19.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17418.08
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.11
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5328.91
p-value of test                       :  6.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  260.28
p-value of test                       :  2.7e-3


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.72
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10281.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:27.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5107.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11507.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.81
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000112345

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.28
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999936785

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:43.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 J (L=10000, r=15)   6.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16416777.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7520
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.06
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.44
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.31
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.24
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908453
  j =  2                              :            45769
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907774
  j =  2                              :            46107
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:19.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:12.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17662.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.34
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.40
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.74
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.44
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.77
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.05
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  148.06
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:28.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000012934

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.62
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999938594

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:05.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17399817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.82
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908570
  j =  2                              :            45712
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907835
  j =  2                              :            46081
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:19.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.57
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.16
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.40
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.71
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  308.44
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  482.89
p-value of test                       :  4.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.51
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.71
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.53
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:27.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4322.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.02
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999927929

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.87
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999977732

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:46.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   4.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18415625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.03
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.70
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46213
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870213
  j =  1                              :        399907579
  j =  2                              :            46203
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46119
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870119
  j =  1                              :        399907764
  j =  2                              :            46115
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:19.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.70
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.85
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.87
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.22
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.27
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.26
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.51
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.62
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.07
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999968312

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.15
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000016708

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:48.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19431433.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:30.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.44
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908794
  j =  2                              :            45600
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    5.65
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:19.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.28
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.30
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.00
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  188.41
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.60
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.34
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.76
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.61
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.19
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:29.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.42
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999972824

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.20
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000033022

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:57.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9992 
 47  MaxOft, t = 16                  0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 983070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.24
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.91
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4849.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908187
  j =  2                              :            45896
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45472
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869472
  j =  1                              :        399909056
  j =  2                              :            45472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.93e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:19.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:15.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:14.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.78
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.17
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.23
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.56
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.75
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    5.56
p-value of test                       :  1.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.03
p-value of test                       :  1.2e-3

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.75
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999902915

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.27
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999915956

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:28.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1179678.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.57
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4858.70
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907614
  j =  2                              :            46190
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907990
  j =  2                              :            46002
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.34
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   71.72
p-value of test                       :  2.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.73
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.84
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.04
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.03
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.58
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.30
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.16
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:30.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3938.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.24
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999894758

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.04
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999977852

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:22.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       2.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2064414.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    3.43
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.80
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.75
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:52.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908420
  j =  2                              :            45787
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45288
p-value of test                       :    0.9971


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869288
  j =  1                              :        399909430
  j =  2                              :            45276
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.25
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.10
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.43
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.74
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.42
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -403.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.22
p-value of test                       :    0.9964

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:31.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12206.89
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.12
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999904490

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.86
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999910826

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:21.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3080222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4531
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.41
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.20
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5267.55
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908045
  j =  2                              :            45973
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908199
  j =  2                              :            45893
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.91
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.83
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.59
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.50
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.17
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.38
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.94
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.30
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.24
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.17
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999991361

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.99
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999994787

Normal statistic for number of bits   :  -0.041
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:56.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4096030.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:39.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.62
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.45
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908710
  j =  2                              :            45636
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908113
  j =  2                              :            45936
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.15e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.49e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.22
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.94
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.56
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.81
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.24
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.77
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.99e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10254.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:31.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12202.77
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.45
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000040627

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000014986

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5111838.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.65
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     804
p-value of test                       :    0.9994    *****

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    3.87
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.69
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  182.76
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.26
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.37
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908055
  j =  2                              :            45965
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908500
  j =  2                              :            45747
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:19.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -1.94e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.20
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.18
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.55
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.18
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.12
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.40
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:27.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999961526

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999963596

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:23.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 92  HammingCorr, L = 30             0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6127646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5552
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:21.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    4.20
p-value of test                       :  7.0e-3

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.38
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.47
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908371
  j =  2                              :            45807
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908236
  j =  2                              :            45876
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:29.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.50
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.22
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.01
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.86
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.17
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -401.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.55
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.90
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:26.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.04
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000017065

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.92
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000032281

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:51.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 J (L=50, r=0)       0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7143454.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:21.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:34.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5192.48
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45391
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869391
  j =  1                              :        399909223
  j =  2                              :            45381
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908293
  j =  2                              :            45852
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.30
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:18.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:12.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:00:12.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.059
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17732.92
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.38
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.49
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.26
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5204.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.13
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.87
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.51
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.33
p-value of test                       :    0.9927


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.32
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.43
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:24.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12249.41
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12156.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.46
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000100384

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999988148

Normal statistic for number of bits   :  -0.094
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:18.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8126494.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:31.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     979
p-value of test                       :  4.9e-3

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.10
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908231
  j =  2                              :            45880
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907957
  j =  2                              :            46017
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:19.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:28.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17777.59
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.25
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.38
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.18
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.27
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.94
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.17
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.43
p-value of test                       :    0.9938

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10320.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999924557

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.95
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000134611

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.78
p-value of test                       :  2.7e-3

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:54.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9142302.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5575
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:31.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.00
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.00
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907793
  j =  2                              :            46096
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908606
  j =  2                              :            45691
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 3.52e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17593.25
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.26
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.41
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.69
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.32
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.73
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.90
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.30
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.77e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.70
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:46.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.10
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.78
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000096301

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.88
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999994262

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:54.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10158110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:31.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.71
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.55
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908009
  j =  2                              :            45991
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.94e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.056
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.16
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.72
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.47
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.25
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.92
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.56
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:03:44.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000113281

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.97
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000094408

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:34.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11173918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:34.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9914


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    3.53
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9977

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.51
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.80
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.94
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908477
  j =  2                              :            45754
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.90e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.67
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.12
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.40
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.63
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.00
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.26
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.92
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:34.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.94
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000225349

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.61
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999796397

Normal statistic for number of bits   :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:10.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12189726.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.50
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.30
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.76
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5182.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907828
  j =  2                              :            46077
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908331
  j =  2                              :            45824
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:19.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:12.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:27.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17114.37
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.44
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.80
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.33
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.53
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.94
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:23.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3930.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.05
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000177184

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.40
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999847997

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:01.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13205534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.65
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908228
  j =  2                              :            45874
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908114
  j =  2                              :            45931
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.45e-4
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:19.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.98
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.86
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.91
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.57
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.54
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.88
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999862997

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999863552

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:34:59.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14221342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4179
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9971

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.34
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46318
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870318
  j =  1                              :        399907368
  j =  2                              :            46310
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.59
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.12
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.43
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.23
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.21
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.55
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.66
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:27.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.32
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999986981

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.79
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999975932

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:03.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15237150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  502.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.71
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.05
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908144
  j =  2                              :            45922
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:19.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:19.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16952.78
p-value of test                       :    0.9950



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.89
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.87
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.48
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.70
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.56
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.52
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.34
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.62
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000006619

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.92
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000033748

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:05.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16252958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:36.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.45
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5169.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46249
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870249
  j =  1                              :        399907509
  j =  2                              :            46235
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908465
  j =  2                              :            45763
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:18.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:12.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:29.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.67
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.41
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.01
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.05
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.11
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.80
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.51
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000131515

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.94
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999949634

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:04.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17268766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7128
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9977

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    4.05
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.95
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7239.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.48
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4789.72
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908046
  j =  2                              :            45974
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908724
  j =  2                              :            45629
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.61e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:18.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.38
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.15
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.67
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.60
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.04
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.66
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.30
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.47
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.57
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.39
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000250870

Normal statistic for number of bits   :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999940454

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:19.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18284574.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n84, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7251.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.27
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.68
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908445
  j =  2                              :            45773
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n84, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908083
  j =  2                              :            45954
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:19.26

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 1.36e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.55
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  8.5e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.98
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.22
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.33
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.08
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.73
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.58
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.83
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.18
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.89
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11578.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.52
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000051256

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.68
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000065608

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n84, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:15.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19300382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7092
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.34
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.83
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.05
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908514
  j =  2                              :            45737
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908506
  j =  2                              :            45744
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.80
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.08
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  573.47
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.39
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.48
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.12
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.97
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.81
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.69
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -403.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.22e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.98
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.36
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.78
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000067219

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.40
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999905663

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:27.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 0.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     113
p-value of test                       :    0.9990    *****

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5223.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:54.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908124
  j =  2                              :            45929
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908647
  j =  2                              :            45666
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.04
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17188.67
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.17
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.65
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.84
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.21
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:30.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.97
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000079420

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.28
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999895931

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:29.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1671173.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7315.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.71
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.07
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:53.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908692
  j =  2                              :            45639
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.97e-4
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  104.87
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.21
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.96
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.61
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.31
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.66
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.37
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.61
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:30.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12205.31
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.45
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000100813

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.32
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000161782

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         : 3.10e-3
p-value of test                       :    0.50

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:53.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2293765.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.17
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.07
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.36
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907861
  j =  2                              :            46065
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45498
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869498
  j =  1                              :        399909007
  j =  2                              :            45492
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-5    *****

Anderson-Darling statistic = A2       :    6.66
p-value of test                       :  5.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:27.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17660.35
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.11
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.62
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.85
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.95
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.96
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.42
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.85
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:31.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5157.29
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999970583

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.26
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999856412

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:31.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               5.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3440645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7098
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    4.48
p-value of test                       :  5.1e-3

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4796.43
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46322
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870322
  j =  1                              :        399907358
  j =  2                              :            46318
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908006
  j =  2                              :            45991
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.55
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.75
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   44.12
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.00
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.95
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.09
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.54
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.46
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000081511

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.72
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999990698

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:59.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4259845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9907

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   31.04
p-value of test                       :  6.1e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5267.60
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:52.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45517
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869517
  j =  1                              :        399908970
  j =  2                              :            45509
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907981
  j =  2                              :            46005
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-4
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    : 1.49e-5
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    5.81
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  5.5e-4    *****

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17123.78
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.65
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.72
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.38
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.14
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.98
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.51
p-value of test                       :  5.9e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.72
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11558.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.41
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999784604

Normal statistic for number of bits   :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.74
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999963449

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:47.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                6.1e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5537797.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:55.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908144
  j =  2                              :            45916
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908917
  j =  2                              :            45531
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17150.81
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.07
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.03
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.56
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.92
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.43
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.78
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.34
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.39
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999901640

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.78
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999974942

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:39.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6422533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.64
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:49.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907863
  j =  2                              :            46064
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907827
  j =  2                              :            46079
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.47e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.18
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.96
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.43
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.73
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.53
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.25
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.47
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.30
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -401.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.20
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   25.64
p-value of test                       :  1.2e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.09
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11524.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.40
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999968114

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.35
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000113302

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:16.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7438365.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.75
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908115
  j =  2                              :            45935
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907569
  j =  2                              :            46211
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  8.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.37
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.23
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.88
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.75
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.60
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.61
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.62
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.22
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.28
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.88
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.17
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 1.71e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.65
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999813983

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.22
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999993713

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8421405.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    3.38
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     966
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     348
p-value of test                       :  3.6e-3

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    4.44
p-value of test                       :  5.3e-3

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.01
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.31
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907942
  j =  2                              :            46023
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908070
  j =  2                              :            45962
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    5.63
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  6.6e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.88
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.13
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4774.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.50
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.59
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.12
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.89
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -401.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.81
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.53
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.24
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4675.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.55
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999955058

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.87
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999926702

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:38.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft, t = 16                  6.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9404445.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.65
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.77
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:56.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908407
  j =  2                              :            45792
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908588
  j =  2                              :            45697
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17760.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.95
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.94
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.85
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.86
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.39
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.20
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9749.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:31.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3920.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.46
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000052114

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.75
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999858599

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    3.22
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Tests on the sum of all N observations
Standardized normal statistic         :  -0.089
p-value of test                       :    0.54

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:41.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10518557.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1557.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.17
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46294
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870294
  j =  1                              :        399907417
  j =  2                              :            46284
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908463
  j =  2                              :            45761
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.52e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.31
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.84
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.74
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.14
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.84
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.16
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.59
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.58
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.41
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -7.64e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.42
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000064186

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000151423

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.6e-4    *****

Anderson-Darling statistic = A2       :    5.06
p-value of test                       :  2.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.77
p-value of test                       :  2.8e-3

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:14.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11534365.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9974

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.55
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.76
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45483
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869483
  j =  1                              :        399909039
  j =  2                              :            45473
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908110
  j =  2                              :            45939
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.73
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.87
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  607.67
p-value of test                       :  6.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.58
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.09
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.29
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.96
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.52
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.51
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:28.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.80
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999937262

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.49
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000046576

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            0.9993 
 76  RandomWalk1 J (L=1000, r=0)     6.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12484637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.85
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.80
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907985
  j =  2                              :            46006
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46250
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870250
  j =  1                              :        399907502
  j =  2                              :            46246
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.96e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.52
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.10
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.32
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.29
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.45
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.29
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.08
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.51
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:28.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.47
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000171664

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.73
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000081547

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.070
p-value of test                       :    0.47

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:04.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13860893.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908259
  j =  2                              :            45863
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908345
  j =  2                              :            45820
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17643.83
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.76
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.37
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.26
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.19
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.14
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.64
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11482.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000016990

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.37
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999971360

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14745629.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908346
  j =  2                              :            45821
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908795
  j =  2                              :            45598
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.64
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.93
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.27
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.67
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.44
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.94
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  256.12
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.87
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.79
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.64
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.80
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9748.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.50
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999977966

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.25
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000020971

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:07.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15761437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997325
  j =  2                              :             1336
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9995    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.86
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.01
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45772
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869772
  j =  1                              :        399908458
  j =  2                              :            45768
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908362
  j =  2                              :            45816
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.69
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.71
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.50
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.21
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.91
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.51
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.83
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.10
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:28.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.68
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999909887

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.60
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999853961

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:48.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16810013.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.32
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907718
  j =  2                              :            46138
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907667
  j =  2                              :            46162
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17511.03
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.84
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.00
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.04
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.96
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.14
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.20
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.70
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.00
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.24
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.60
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.00
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.85
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.72
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999921689

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000046648

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.94

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:42.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17825821.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   26.83
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.44
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907540
  j =  2                              :            46221
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17613.53
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.50
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.73
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.68
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.09
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.13
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.15
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.73
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9757.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 9.70e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:28.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.43
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999977720

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.98
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999885467

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:45.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18907165.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.77
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:10.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.33
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.91
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.64
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:52.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908204
  j =  2                              :            45892
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908123
  j =  2                              :            45937
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  7.3e-4    *****

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.11
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.85
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  101.23
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.47
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.47
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.01
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.49
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.49
p-value of test                       :  9.1e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.95
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000154159

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.00
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000148381

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:04.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19857437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1234
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334354
  j =  1                              :        599997532
  j =  2                              :             1234
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5273
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.50
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.93
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.41
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:58.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907894
  j =  2                              :            46047
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    5.37
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  9.5e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.51
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17609.54
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.57
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.45
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.30
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.87
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.41
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.57
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.02
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.57
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.61
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000035422

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.35
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000225103

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:39.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9998 
 47  MaxOft, t = 16                  9.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 32769.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  369.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.91
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.88
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45434
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869434
  j =  1                              :        399909134
  j =  2                              :            45430
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907884
  j =  2                              :            46049
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17838.88
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.06
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.47
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.20
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.20
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.55
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.33
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.43
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.12
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.03
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.14
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.65
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.66
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.62
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4343.13
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.30
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000004171

Normal statistic for number of bits   :   0.033
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.26
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000031702

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:54.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1802260.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.36
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    4.38
p-value of test                       :  5.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.96
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.75
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.25
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907801
  j =  2                              :            46095
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17094.43
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.89
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.26
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  616.22
p-value of test                       :  2.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.59
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5194.32
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.03
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.45
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.13
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.32
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.10
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999961034

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.18
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000000853

Normal statistic for number of bits   : 6.74e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:48.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    2.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2621460.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.36
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.37
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908158
  j =  2                              :            45915
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908114
  j =  2                              :            45943
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.32
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    7.86
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.38
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.92
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.63
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  146.56
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.15
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.33
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.53
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.95
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.73
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.95
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999829820

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.46
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999892895

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:56.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3604500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908402
  j =  2                              :            45796
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908607
  j =  2                              :            45692
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.96
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.48
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.01
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.01
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.15
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.43
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.68
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.93
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.97
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.58
p-value of test                       :  6.4e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.74
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.35
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999874439

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999967721

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:46.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4489236.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    3.63
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     967
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  373.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7402.17
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.92
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5158.95
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:56.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907588
  j =  2                              :            46203
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907802
  j =  2                              :            46096
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17038.82
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.03
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.98
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.81
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.47
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.02
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.65
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.48
p-value of test                       :    0.9931

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.32
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.33
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999901616

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.87
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000084850

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:36.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5505044.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4191
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.36
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:00.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908071
  j =  2                              :            45960
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.61
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.25
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.80
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.32
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.55
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.7e-3

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.52
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.86
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11443.54
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.98
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999988712

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.41
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000113368

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    5.64
p-value of test                       :  1.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.15
p-value of test                       :  8.3e-4    *****

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:28.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 104  AutoCor, d=3, r=0               8.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6684696.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    4.19
p-value of test                       :  7.0e-3

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.21
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7281.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.83
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908047
  j =  2                              :            45972
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908394
  j =  2                              :            45800
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17652.00
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.41
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.97
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.93
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.71
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.82
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.82
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -401.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.28
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10272.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.65
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000108700

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.79
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000152761

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7733272.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7117
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    4.65
p-value of test                       :  4.2e-3

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.52
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.07
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908533
  j =  2                              :            45729
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907941
  j =  2                              :            46025
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.96
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.25
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.62
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.49
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.29
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.83
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.85
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.58
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.61
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5128.62
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000003238

Normal statistic for number of bits   :   0.026
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.46
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999954011

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:34.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8650776.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    4.53
p-value of test                       :  4.9e-3

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.26
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.56
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908024
  j =  2                              :            45982
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908285
  j =  2                              :            45853
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.14
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.51
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.41
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.76
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.10
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5225.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.22
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.36
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.63
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.25
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.05
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000061894

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999874880

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:04.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9601048.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.86
p-value of test                       :  3.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    3.37
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.08
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46330
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870330
  j =  1                              :        399907343
  j =  2                              :            46324
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908582
  j =  2                              :            45703
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.83
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.80
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.02
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.92
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.44
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.81
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.94
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.49
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.24
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.93
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000104086

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.26
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999923456

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.51
p-value of test                       :  6.1e-3

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10747928.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6777.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908221
  j =  2                              :            45882
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908436
  j =  2                              :            45779
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    5.32
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.96
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17068.04
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.66
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.29
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.09
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.95
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.95
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.62
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.90
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.26
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5132.75
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.52
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000122785

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.05
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999960041

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    3.45
p-value of test                       :  2.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:06.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11698200.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.23
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908628
  j =  2                              :            45677
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907828
  j =  2                              :            46074
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.69
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  411.85
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.39
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.34
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.09
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.39
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.57
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12092.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.92
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000037324

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.14
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999958433

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:27.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12714008.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    3.85
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    7.38
p-value of test                       :  2.3e-4    *****

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9978

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  297.18
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6914.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908206
  j =  2                              :            45897
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907906
  j =  2                              :            46047
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.38
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.72
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.23
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9901

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5169.03
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11629.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.78
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999946364

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.59
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000002632

Normal statistic for number of bits   :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:42.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          2.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13598744.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:29.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     818
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    3.15
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.29
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.69
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908673
  j =  2                              :            45659
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908683
  j =  2                              :            45651
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.13
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.81
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.09
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5251.63
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.90
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.20
p-value of test                       :  6.6e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.96
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.87
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999997460

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   90.86
p-value of test                       :  1.3e-3


-----------------------------------------------
Total number of bits:  7999986375

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:27.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14712856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.13
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908198
  j =  2                              :            45889
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908194
  j =  2                              :            45900
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17648.40
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.41
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.86
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.57
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.04
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -401.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10215.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:29.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.38
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000114115

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.35
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999960083

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:27.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16220184.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.82
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.57
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908234
  j =  2                              :            45877
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45358
p-value of test                       :    0.9926


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869358
  j =  1                              :        399909286
  j =  2                              :            45354
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.99e-4
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:15.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17374.26
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.36
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.86
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.72
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.08
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.36
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.73
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:29.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   99.19
p-value of test                       :  1.7e-4    *****


-----------------------------------------------
Total number of bits:  8000260887

Normal statistic for number of bits   :    2.06
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.09
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999991154

Normal statistic for number of bits   :  -0.070
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:30.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 101  Run of bits, r = 0              1.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17203224.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997297
  j =  2                              :             1350
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.96
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:29.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.01
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.61
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908735
  j =  2                              :            45631
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17203.63
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.75
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.68
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.83
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.16
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.31
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.59
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.69
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.64
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10404.19
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -4.94e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.97
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12103.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.51
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999937925

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.69
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999957488

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:05.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18219032.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.67
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.70
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.60
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907826
  j =  2                              :            46081
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.60
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17213.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.44
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.96
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.00
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.10
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.07
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.61
p-value of test                       :  4.5e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.25
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.63
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999978788

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.08
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000047788

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:06.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19202072.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7219.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.80
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.50
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46199
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870199
  j =  1                              :        399907607
  j =  2                              :            46189
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908784
  j =  2                              :            45605
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.97
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.57
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.63
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  206.78
p-value of test                       :  7.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.33
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5194.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.14
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.73
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.06
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.17
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  142.99
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9644.27
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.54
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4325.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.53
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000136354

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.85
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000061441

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:09.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 M (L=1000, r=20)    7.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 88  PeriodsInStrings, r = 0         0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20217880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.74
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908243
  j =  2                              :            45868
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908303
  j =  2                              :            45844
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:28.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.78
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17124.85
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.53
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.46
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.42
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.40
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.62
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.51
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10343.87
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -6.28e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4318.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11617.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.99
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000027721

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.68
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999994121

Normal statistic for number of bits   :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:33.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 65538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.89
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:57.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907811
  j =  2                              :            46087
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908634
  j =  2                              :            45680
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.95
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.73
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.52
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.13
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.36
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.23
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000039568

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.08
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999920963

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:46.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1179650.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5540
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7224.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.48
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.14
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.27
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908006
  j =  2                              :            45991
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908346
  j =  2                              :            45821
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.64
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.20
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.18
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.31
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.31
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.40
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.49
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.92
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.41
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.07
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000086887

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.91
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999938033

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:52.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2523138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1337.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.66
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.33
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46219
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870219
  j =  1                              :        399907565
  j =  2                              :            46213
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908343
  j =  2                              :            45821
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   53.83
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17753.83
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.97
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.35
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.63
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.62
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.71
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.84
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.78
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.10
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9702.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000066529

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.37
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000046843

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.53

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:46.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3276802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.71
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    6.17
p-value of test                       :  8.3e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.79
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.26
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908095
  j =  2                              :            45948
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908598
  j =  2                              :            45698
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.89
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.03
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.14
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.98
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.68
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.08
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.30
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.01
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.14
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.42
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999909680

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.70
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999993503

Normal statistic for number of bits   :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:58.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         8.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4390914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9950


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    3.55
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.48
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.48
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46287
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870287
  j =  1                              :        399907429
  j =  2                              :            46281
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45408
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869408
  j =  1                              :        399909191
  j =  2                              :            45394
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.48
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.06
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   50.64
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.90
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.87
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.94
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.84
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5170.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.00
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.56
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.44
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.98
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5090.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.75
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999997679

Normal statistic for number of bits   :  -0.018
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.11
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999982925

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:32.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5439490.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.04
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908384
  j =  2                              :            45805
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908098
  j =  2                              :            45948
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.48e-4
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.64
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.29
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.03
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.57
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.28
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.56
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.80
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.05
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.01
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.82
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999905711

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.61
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000019582

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:08.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6258690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:28.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.34
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908824
  j =  2                              :            45579
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908110
  j =  2                              :            45939
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.75
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.25
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.88
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.45
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.15
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.46
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.03
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.18
p-value of test                       :  7.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.42
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000057595

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.88
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999901727

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:23.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 92  HammingCorr, L = 30             7.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7241730.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     653
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.26
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908202
  j =  2                              :            45893
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908336
  j =  2                              :            45829
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.60
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.82
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  270.99
p-value of test                       :  6.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.19
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.09
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.42
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.02
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3879.83
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.21
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999956147

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.00
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000170347

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:03.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    6.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8290306.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5252
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9907

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.98
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.94
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908423
  j =  2                              :            45778
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907781
  j =  2                              :            46105
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    5.13
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.52
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.80
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.09
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.72
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.16
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.75
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  474.73
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.61
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.76
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.76
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000034675

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.84
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999987410

Normal statistic for number of bits   :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:20.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9306114.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     808
p-value of test                       :    0.9990    *****

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     542
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.69
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.81
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:57.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908528
  j =  2                              :            45721
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908315
  j =  2                              :            45838
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.66e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.68
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.32
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.51
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.01
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.13
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.73
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.93
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.06
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.12
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000045493

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.25
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999979094

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.51
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:51.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10321922.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7067
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.97
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908228
  j =  2                              :            45880
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.01
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.86
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.65
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   52.55
p-value of test                       :  1.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.80
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.94
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12097.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.17
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000037306

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.22
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999880316

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    2.60
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    2.87
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:27.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11337730.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.25
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907963
  j =  2                              :            46017
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908759
  j =  2                              :            45616
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9982

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.33
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.69
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.70
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.08
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.88
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.02
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.65
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.35
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:28.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4699.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.85
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000072166

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.69
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000030748

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9913

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:06.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12353538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1485
p-value of test                       :  6.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334605
  j =  1                              :        599997030
  j =  2                              :             1485
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    3.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.39
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:56.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907699
  j =  2                              :            46140
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908445
  j =  2                              :            45773
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:15.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.35e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:29.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.35
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17288.87
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.23
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.85
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.72
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.48
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9754.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.17
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999977960

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.42
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999945884

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.63e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.87
p-value of test                       :    0.9980

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:38.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           6.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13369346.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   26.10
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:54.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908281
  j =  2                              :            45852
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908615
  j =  2                              :            45685
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-5
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:19.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:28.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   16.40
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.41
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.80
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.11
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.44
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.46
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.70
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.47
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.76
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.30
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.39
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999890333

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.44
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000016222

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:38.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 32  CouponCollector, r = 20         0.9995 
 68  MatrixRank, L=1000, r=0         9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14385154.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    4.82
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.47
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4913.94
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908699
  j =  2                              :            45646
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908579
  j =  2                              :            45709
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:28.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.78
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.23
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.68
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.33
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.09
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.29
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.21
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.01
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999972506

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.14
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000081490

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    3.24
p-value of test                       :  6.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:45.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15400962.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7329.30
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.70
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.69
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908492
  j =  2                              :            45751
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908437
  j =  2                              :            45771
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.86
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.60
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.50
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.60
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.19
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.86
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.07
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.38
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999991763

Normal statistic for number of bits   :  -0.065
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.72
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000034123

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.036
p-value of test                       :    0.51

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:16.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16384002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4113
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.39
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.26
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.73
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:59.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907918
  j =  2                              :            46035
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45472
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869472
  j =  1                              :        399909057
  j =  2                              :            45470
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17235.18
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.22
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.06
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.40
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.17
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.85
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.05
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.33
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.37
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10233.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4321.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.64
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000042730

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.84
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000124666

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:37.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17399810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5285.28
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908530
  j =  2                              :            45729
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17861.48
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.23
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.84
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.68
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.00
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.89
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.31
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.87
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.84
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.48
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.36
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   89.68
p-value of test                       :  1.6e-3


-----------------------------------------------
Total number of bits:  8000001099

Normal statistic for number of bits   : 8.69e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.39
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999993950

Normal statistic for number of bits   :  -0.048
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:19.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18415618.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.71
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  358.89
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:29.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46274
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870274
  j =  1                              :        399907455
  j =  2                              :            46268
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908344
  j =  2                              :            45825
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.74e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.69
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.06
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.98
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.87
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.33
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10328.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.05
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000083821

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.89
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999944459

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:35.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19431426.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  340.29
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.02
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.29
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.24
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:56.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908763
  j =  2                              :            45614
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908286
  j =  2                              :            45854
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.04
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.52
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.95
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.56
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.56
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.46
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5199.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.54
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.13
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.96
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.37
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000071470

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.30
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999977198

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:00.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.4e-4
 35  Gap, r = 25                     0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 98307.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.31
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4878.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908366
  j =  2                              :            45814
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908217
  j =  2                              :            45887
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.57e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17163.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.26
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.91
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.75
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:31.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11514.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.59
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000036325

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.56
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000130858

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:05.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1409027.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7357.05
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-4
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.54
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  100.28
p-value of test                       :  8.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.15
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908127
  j =  2                              :            45932
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908534
  j =  2                              :            45724
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   70.86
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17185.16
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.94
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.60
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.17
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.27
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.71
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999915695

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.77
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000138988

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:34.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2359299.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1238
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334358
  j =  1                              :        599997524
  j =  2                              :             1238
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.11
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4861.47
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908311
  j =  2                              :            45840
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45478
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869478
  j =  1                              :        399909047
  j =  2                              :            45472
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.24
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.33
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.54
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.89
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.72
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.84
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4842.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.24
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.79
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.93
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  255.60
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.97
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.22
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999844490

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000041470

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3342339.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7532
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9943

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.35
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.97
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908886
  j =  2                              :            45554
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908516
  j =  2                              :            45739
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17268.72
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.64
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.03
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.71
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.88
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11550.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.55
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999855842

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.91
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999999050

Normal statistic for number of bits   : -7.51e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:24.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4554755.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.09
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.86
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.30
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.16
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907959
  j =  2                              :            46016
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908492
  j =  2                              :            45751
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.14
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.38
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.31
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  595.09
p-value of test                       :  2.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.66
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.19
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.89
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.66
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.81
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.90
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.72
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.79e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9688.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.54
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999908876

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.49
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000096352

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:12.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5373955.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.64
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.78
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    4.19
p-value of test                       :  7.1e-3

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.56
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7267.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.47
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907947
  j =  2                              :            46019
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908230
  j =  2                              :            45882
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.82
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.76
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.37
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.54
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.63
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.28
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.98
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  261.97
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.46
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.91
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:33.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.76
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000083812

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.71
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000054619

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6782979.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7339.36
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.69
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.32
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908109
  j =  2                              :            45938
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46261
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870261
  j =  1                              :        399907484
  j =  2                              :            46249
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.16e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.30
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.39
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  116.41
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.49
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.66
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.79
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    2.77
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.11
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.20
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000048388

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.47
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000056602

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7602179.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.32
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.20
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908805
  j =  2                              :            45593
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908362
  j =  2                              :            45816
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17204.89
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.78
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.73
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.28
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.91
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.98
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.02
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.57
p-value of test                       :    0.9914

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.13
p-value of test                       :  8.1e-3


-----------------------------------------------
Total number of bits:  8000007048

Normal statistic for number of bits   :   0.056
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.45
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999857876

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:18.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8617987.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7175.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.34
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.58
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908654
  j =  2                              :            45670
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46306
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870306
  j =  1                              :        399907393
  j =  2                              :            46296
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.93
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.97
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.48
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.11
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.23
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9712.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 2.27e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999998243

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.70
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999910544

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:00.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9535516.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5297
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.74
p-value of test                       :  1.3e-3

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.87
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.01
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.71
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45580
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869580
  j =  1                              :        399908845
  j =  2                              :            45570
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908500
  j =  2                              :            45744
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17522.74
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.90
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.62
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.49
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  145.79
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.32
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.64
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.12
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9613.68
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:31.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.82
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.16
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000123955

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.11
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000145876

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:32.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10485788.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:18.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.45
p-value of test                       :  5.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:20.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.53
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.41
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907971
  j =  2                              :            46007
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908190
  j =  2                              :            45899
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17103.40
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.93
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.65
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.13
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.53
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.81
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:30.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.07
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000046129

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.12
p-value of test                       :  9.9e-3


-----------------------------------------------
Total number of bits:  7999966746

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:34.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11501596.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7520
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.33
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.58
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.45
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:54.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908324
  j =  2                              :            45832
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908554
  j =  2                              :            45717
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17689.05
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.84
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.66
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.57
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.89
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.32
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  453.44
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.53
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.92
p-value of test                       :  4.8e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.41
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9596.42
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:29.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000016777

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.83
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999862739

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:56.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 81  LinearComp, r = 0               4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13008924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:37.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.23
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.24
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.48
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908637
  j =  2                              :            45677
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908693
  j =  2                              :            45649
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  6.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    5.38
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    4.82
p-value of test                       :  3.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.05
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.33
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.38
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.02
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.60
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.94
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.27
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.96
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.02
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   40.54
p-value of test                       :  5.8e-5    *****


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.24
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.15
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4622.09
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.52
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.41
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999953291

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.78
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000015964

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:46.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               5.8e-5
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13926428.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.40
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.07
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908488
  j =  2                              :            45747
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907884
  j =  2                              :            46055
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.07
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.98
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.39
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.15
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.76
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.07
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.63
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:03:28.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.17
p-value of test                       :    0.9920


-----------------------------------------------
Total number of bits:  8000037978

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.22
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999902069

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:48.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14778396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1517
p-value of test                       :  2.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334637
  j =  1                              :        599996966
  j =  2                              :             1517
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4490
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.22
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.78
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4868.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45547
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869547
  j =  1                              :        399908910
  j =  2                              :            45539
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908673
  j =  2                              :            45659
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.91
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.86
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.28
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.58
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.65
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.07
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.82
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.62
p-value of test                       :  6.3e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.26
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:28.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.22
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000036769

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.62
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000042310

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:50.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           2.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15794204.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9939

Test on the Nm values of W_{n,i}(mNP1):    5.10
p-value of test                       :  2.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:20.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.27
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4858.66
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46416
p-value of test                       :  6.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870416
  j =  1                              :        399907174
  j =  2                              :            46404
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46137
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870137
  j =  1                              :        399907728
  j =  2                              :            46133
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:27.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.31
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9982

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16978.82
p-value of test                       :    0.9925



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.96
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.72
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.62
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.07
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.31
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5214.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.64
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.71
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -401.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.64
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:29.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000018007

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.87
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000048508

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16777244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.20
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  163.77
p-value of test                       :  4.1e-3


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908761
  j =  2                              :            45615
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907945
  j =  2                              :            46026
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17182.72
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.09
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.28
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.95
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.09
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.10
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.11
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.18
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -401.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.82
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:29.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.05
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000017119

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.66
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999946940

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:59.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18186268.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    4.76
p-value of test                       :  3.7e-3

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.21
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.10
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.64
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:49.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907794
  j =  2                              :            46094
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45567
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869567
  j =  1                              :        399908869
  j =  2                              :            45561
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.08e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17349.89
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.86
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.09
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.01
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.05
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.25
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.21
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.62
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.13
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:30.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.38
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000218767

Normal statistic for number of bits   :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.31
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000030334

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:57.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19103772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4180
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.58
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    3.55
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.96
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:47.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45416
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869416
  j =  1                              :        399909171
  j =  2                              :            45410
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46306
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870306
  j =  1                              :        399907390
  j =  2                              :            46302
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  1.2e-4    *****

Anderson-Darling statistic = A2       :    7.75
p-value of test                       :  1.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.53e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.48
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.11
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.11
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.48
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.82
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.32
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -401.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.46
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.23
p-value of test                       :  6.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.27
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12080.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.04
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000062299

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.55
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999854030

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:06.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft AD, t = 32               1.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 92  HammingCorr, L = 30             6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20054044.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.58
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908395
  j =  2                              :            45798
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46183
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870183
  j =  1                              :        399907638
  j =  2                              :            46175
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.38e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:29.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16956.53
p-value of test                       :    0.9947



-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.59
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.38
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5200.32
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.92
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.91
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.19
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.44
p-value of test                       :    0.9927

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.88
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999931337

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.92
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999877757

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:09.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 131076.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.82
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.39
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.03
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907947
  j =  2                              :            46022
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.67e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.61
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.71
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.88
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.50
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.01
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.32
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.64
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.37
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12157.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.22
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999999062

Normal statistic for number of bits   : -7.42e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.97
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000052012

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : 4.92e-3
p-value of test                       :    0.50

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:49.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1572868.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    6.46
p-value of test                       :  6.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7225.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.44
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908338
  j =  2                              :            45822
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908602
  j =  2                              :            45696
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.98
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.80
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   72.71
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.98
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.75
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.89
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.53
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999967454

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.79
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999988976

Normal statistic for number of bits   :  -0.087
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:43.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        6.1e-4
 75  RandomWalk1 M (L=50, r=25)      1.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2326532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5305
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    2.97
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6842.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:29.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.90
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5144.30
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908198
  j =  2                              :            45892
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908551
  j =  2                              :            45720
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-5
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.34
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.45
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.40
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.04
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.95
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.63
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.97
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.62
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999951098

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.88
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000041908

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    2.59
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:00.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3407898.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.50
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:32.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.77
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.62
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46271
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870271
  j =  1                              :        399907460
  j =  2                              :            46267
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908401
  j =  2                              :            45798
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9939


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17561.44
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.55
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.86
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.22
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4809.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.85
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.53
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.02
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:35.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.06
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000034618

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.74
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999910349

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:48.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4194330.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1491
p-value of test                       :  3.7e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334611
  j =  1                              :        599997018
  j =  2                              :             1491
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:31.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.52
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908376
  j =  2                              :            45809
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45537
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869537
  j =  1                              :        399908930
  j =  2                              :            45529
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.67
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.04
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.23
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.09
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.31
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.68
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  302.80
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.21
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.46
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.91
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.58
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999784298

Normal statistic for number of bits   :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.07
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999880562

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.20

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:13.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           3.7e-4
 79  RandomWalk1 H (L=10000, r=15)   0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5210138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.89
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.98
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4915.92
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:54.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908692
  j =  2                              :            45648
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908235
  j =  2                              :            45875
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17653.77
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.97
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.12
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.79
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.65
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.42
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.97
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.01
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.18
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999954995

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.81
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000015202

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.49
p-value of test                       :    0.9936

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:05.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27                0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6291482.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7597
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.21
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908585
  j =  2                              :            45697
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907828
  j =  2                              :            46080
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.14
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17119.43
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.42
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.60
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.58
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.88
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.22
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4307.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999877742

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.53
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000033463

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:16.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        6.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7340058.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1532
p-value of test                       :  4.4e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334652
  j =  1                              :        599996936
  j =  2                              :             1532
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5238
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9963


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1333.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.26
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5202.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908139
  j =  2                              :            45926
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908879
  j =  2                              :            45553
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.37e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    : 1.41e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.04
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.04
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.97
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.60
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.89
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.31
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.33
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.54
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999995519

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.51
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999849140

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:41.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           4.4e-6
 25  ClosePairs mNP2S, t = 16        0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8355866.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9981


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.92
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4840.41
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908391
  j =  2                              :            45800
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907676
  j =  2                              :            46153
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  3.3e-4    *****

Anderson-Darling statistic = A2       :    7.64
p-value of test                       :  1.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.07
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17843.54
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.78
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.59
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.98
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.67
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.45
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.78
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.19
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4340.82
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.89
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000052156

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.88
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999933251

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:20.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                1.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9371674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.79
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5235.36
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:56.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46374
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870374
  j =  1                              :        399907254
  j =  2                              :            46370
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908018
  j =  2                              :            45985
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.43
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.40
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17238.96
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.78
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.95
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  497.48
p-value of test                       :  8.1e-5    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.60
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.13
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.50
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.33
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.25
p-value of test                       :    0.9961

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:34.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.13
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999911255

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.23
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000008920

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.019
p-value of test                       :    0.51

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 M (L=10000, r=0)    8.1e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10354714.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.71
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908397
  j =  2                              :            45797
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.58
p-value of test                       :  1.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.94
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.87
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.29
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.05
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.26
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.49
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.67
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.96
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.90
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  146.06
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    : 2.57e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4662.42
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.07
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000029251

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.46
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999904730

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:33.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               1.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11370522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.69
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.90
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.62
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908084
  j =  2                              :            45952
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908557
  j =  2                              :            45717
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:19.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.26
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.81
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.13
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.28
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.09
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.09
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.29
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.58
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.02
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.49
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:03:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12048.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.97
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999970055

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.02
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000097711

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:23.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12386330.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.25
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908686
  j =  2                              :            45654
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908599
  j =  2                              :            45693
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17602.34
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.96
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.48
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.32
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.16
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.97
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.01
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.36
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.04
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.34
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.61
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:26.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.80
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999873296

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.86
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999881306

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:50.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13402138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.07
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.62
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907647
  j =  2                              :            46172
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908756
  j =  2                              :            45619
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.17
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.41
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  582.01
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.24
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.19
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.73
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.05
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.63
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.29
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000000328

Normal statistic for number of bits   : 2.59e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.91
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000031552

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:34.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14450714.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9925

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.60
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908485
  j =  2                              :            45747
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908280
  j =  2                              :            45857
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.97
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.51
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.66
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  465.50
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.93
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.38
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.99
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.40
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.41
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999986264

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.03
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000006808

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:44.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15466522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.06
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     183
p-value of test                       :  5.0e-3

Stat. AD (mNP2)                       :    3.68
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.36
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.12
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:55.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45585
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869585
  j =  1                              :        399908834
  j =  2                              :            45577
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908664
  j =  2                              :            45665
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.21
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.25
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.23
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.34
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.18
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.92
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.57
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.11
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  305.42
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.93
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:26.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.92
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.09
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000088663

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.23
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999904019

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:15.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16482330.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1521
p-value of test                       :  1.6e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334641
  j =  1                              :        599996958
  j =  2                              :             1521
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7534
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.64
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1540.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.36
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908172
  j =  2                              :            45911
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908233
  j =  2                              :            45876
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  5.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 3.99e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.61
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.96
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.96
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.24
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.47
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.48
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.08
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -403.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.23
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.82
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11538.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.86
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000046549

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.00
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000010645

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:59.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9996 
 12  CollisionOver, t = 21           1.6e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17498138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    3.35
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1333.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908235
  j =  2                              :            45875
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908109
  j =  2                              :            45944
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:12.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:28.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.32
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.86
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.36
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.34
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.74
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.92
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.31
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.75
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.08
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:33.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.69
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999940157

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.95
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000023569

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:09.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18513946.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    3.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.61
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5279.78
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908452
  j =  2                              :            45768
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908467
  j =  2                              :            45762
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.70
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.57
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.69
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.21
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.82
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.41
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.14
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.61
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.24
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3897.79
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.18
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999888851

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.11
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000016009

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:47.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19529754.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.45
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.93
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.47
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:58.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908584
  j =  2                              :            45705
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908446
  j =  2                              :            45774
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.30e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16918.14
p-value of test                       :    0.9972



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.65
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.35
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.14
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.11
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.66
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.10
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9711.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.62
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.46
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000090511

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.30
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999862598

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:21.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 163845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6864.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.35
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.66
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909128
  j =  2                              :            45430
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907924
  j =  2                              :            46032
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17571.86
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.01
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.53
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.68
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.62
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999904496

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.40
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999956708

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:28.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1638400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.89
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6904.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.05
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46079
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870079
  j =  1                              :        399907846
  j =  2                              :            46071
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   15.86
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.72
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.09
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.71
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.44
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4842.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  449.63
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.04
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3911.95
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.25
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999917870

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.49
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999974201

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         : -7.42e-3
p-value of test                       :    0.50

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:11.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2719744.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7555
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.79
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.63
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.05
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908531
  j =  2                              :            45727
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908509
  j =  2                              :            45741
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:29.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:29.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17344.60
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.30
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.26
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.89
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.95
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.27
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.00
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999962537

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.08
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999984194

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:21.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3571712.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5556
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4198
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.45
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.51
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908083
  j =  2                              :            45957
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908565
  j =  2                              :            45713
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.56
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.04
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.19
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.87
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.33
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.96
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.61
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.49
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.48
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3938.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3906.56
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.34
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000012796

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.43
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999922352

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.063
p-value of test                       :    0.53

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:27.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4587520.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   32.85
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.50
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908697
  j =  2                              :            45650
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46358
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870358
  j =  1                              :        399907286
  j =  2                              :            46354
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.13
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.14
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.45
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.66
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.51
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.44
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:32.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5105.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.82
p-value of test                       :  7.1e-3


-----------------------------------------------
Total number of bits:  8000031309

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.73
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000037825

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         : -9.36e-3
p-value of test                       :    0.50

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:30.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5406720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9933

Stat. AD after spacings (mNP2-S)      :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.89
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6909.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.22
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.44
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907986
  j =  2                              :            45998
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908225
  j =  2                              :            45883
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.23
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.32
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.21
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.44
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.64
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.02
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999968072

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.85
p-value of test                       :  8.6e-3


-----------------------------------------------
Total number of bits:  8000054628

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:01.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6488064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5272
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    3.40
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.35
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.75
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.41
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908428
  j =  2                              :            45786
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.54e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  102.46
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.93
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.38
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.45
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.39
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.76
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.57
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.53
p-value of test                       :  5.8e-3

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:32.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.59
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999921296

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.82
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000055336

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:58.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7864320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1337.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.49
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5243.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908591
  j =  2                              :            45700
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908243
  j =  2                              :            45874
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.90
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.68
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.19
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.72
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.51
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.48
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.73
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.41
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.98
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10314.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.05
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000025624

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.78
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000078496

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.81

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8749056.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.26
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.06
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.72
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4891.56
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:59.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46197
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870197
  j =  1                              :        399907610
  j =  2                              :            46189
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 5.18e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.26
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.49
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.62
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.25
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.63
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.45
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.77
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.51
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.55
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.06
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.15
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999918224

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.20
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999984653

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:35.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9797632.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9950

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.77
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.81
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907857
  j =  2                              :            46064
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908394
  j =  2                              :            45797
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17720.94
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.26
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.55
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.09
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.52
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.53
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.27
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    2.41
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.34
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000037225

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.47
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999951269

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:53.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10813440.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.87
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.00
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.20
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5264.33
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907752
  j =  2                              :            46121
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908031
  j =  2                              :            45974
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.12e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.57
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.62
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.86
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.35
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.38
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5260.92
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.77
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.24
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.60
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.58
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.06
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.14
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.66
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000029560

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999868415

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11763712.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7540
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    3.70
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     657
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.28
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:37.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.82
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.37
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1316.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6855.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.68
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.31
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.13
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908754
  j =  2                              :            45617
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908116
  j =  2                              :            45933
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17107.67
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.15
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.23
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.24
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.22
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.86
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.97
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.17
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.51
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000014878

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.92
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999962324

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:26.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12746752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5531
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.98
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.70
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908821
  j =  2                              :            45579
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907602
  j =  2                              :            46196
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17196.77
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.45
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.71
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.51
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.11
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.64
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.25
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9770.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:28.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.42
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000162517

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.55
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999911459

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13631488.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.37
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.89
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.67
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45580
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869580
  j =  1                              :        399908846
  j =  2                              :            45568
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907809
  j =  2                              :            46091
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17781.62
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.58
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.97
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.35
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.63
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.19
p-value of test                       :  2.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.95
p-value of test                       :    0.9984

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.07
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000087271

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.84
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999950684

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:06.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14680064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4490
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   96.71
p-value of test                       :  3.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.57
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.54
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.95
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908061
  j =  2                              :            45965
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908237
  j =  2                              :            45874
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.42
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17370.88
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.10
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   67.44
p-value of test                       :  8.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.79
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.96
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.68
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.15
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.14
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:29.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4627.30
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12091.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.26
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999959801

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.33
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000013378

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:50.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 32  CouponCollector, r = 20         3.2e-4
 75  RandomWalk1 M (L=50, r=25)      8.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15859712.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.14
p-value of test                       :  7.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.60
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.57
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.29
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.49
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:52.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908041
  j =  2                              :            45972
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908700
  j =  2                              :            45647
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.21
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.23
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.38
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.85
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.33
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.33
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.94
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.18
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999955112

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.63
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000097018

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:02.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16908288.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5260
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9959

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.09
p-value of test                       :  8.3e-3

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.33
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.03
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908351
  j =  2                              :            45820
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46479
p-value of test                       :  2.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870479
  j =  1                              :        399907048
  j =  2                              :            46467
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.95
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.44
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.00
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5218.19
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.99
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.66
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.08
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.31
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.43
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999909092

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.76
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000011215

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:53.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17760256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5264
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.94
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.04
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908407
  j =  2                              :            45786
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46317
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870317
  j =  1                              :        399907369
  j =  2                              :            46311
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.59
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.91
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.09
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.81
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.42
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.03
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.52
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.77
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.43
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999993809

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.94
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000139312

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:17.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18808832.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5300
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7512
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.39
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.66
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:47.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907992
  j =  2                              :            46001
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.44e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.45e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.56
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.68
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.33
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.68
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  307.97
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.84
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.85
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.82
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000072058

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.86
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999962285

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:07.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20021248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    3.68
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6828.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.64
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.02
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.79
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908855
  j =  2                              :            45565
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908510
  j =  2                              :            45736
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.89
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.11
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.09
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.11
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11459.33
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12231.10
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.26
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999942911

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999882395

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:19.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 196614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    5.29
p-value of test                       :  2.1e-3

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.45
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.16
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:55.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46170
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870170
  j =  1                              :        399907665
  j =  2                              :            46160
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.68
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.96
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.28
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.34
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.97
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5233.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.67
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10233.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5088.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5063.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12052.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.56
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000089314

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.39
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000046720

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:56.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1081350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:11.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.85
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:52.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908260
  j =  2                              :            45870
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908125
  j =  2                              :            45930
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.17
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.75
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.15
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.03
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999857336

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.48
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999964259

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:38.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2162718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.20
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.99
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.07
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5169.75
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908134
  j =  2                              :            45933
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908240
  j =  2                              :            45880
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.28e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.81
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.05
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.16
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.25
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.63
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5231.87
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.38
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.42
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 6.82e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12241.30
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.36
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000089275

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.76
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999881330

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:54.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3538974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.36
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.34
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908118
  j =  2                              :            45941
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908604
  j =  2                              :            45692
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.37
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.76
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.58
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.09
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5216.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.54
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -403.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.43
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12273.92
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.68
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000015145

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.85
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999896507

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:42.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4325395.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:38.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   18.63
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907842
  j =  2                              :            46073
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907862
  j =  2                              :            46063
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.90
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.96
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.97
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.46
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.34
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.99
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.43
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12089.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.17
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000096874

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.18
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999971849

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:51.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5603347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    4.28
p-value of test                       :  6.3e-3

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    7.17
p-value of test                       :  3.0e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.64
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.65
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:59.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907883
  j =  2                              :            46048
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908606
  j =  2                              :            45691
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.42
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.55
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.42
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.17
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.15
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.06
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.23
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    5.40
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10438.13
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.27
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000041434

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.13
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999985055

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:34.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           3.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6815763.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.78
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907816
  j =  2                              :            46086
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45411
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869411
  j =  1                              :        399909182
  j =  2                              :            45403
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17668.92
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.97
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.63
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.79
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.69
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  308.34
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.92
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.32
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.11
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.77
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9695.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11514.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.90
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999824243

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.24
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999997532

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7667731.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.39
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908564
  j =  2                              :            45715
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908719
  j =  2                              :            45636
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17136.22
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.59
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.57
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.82
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.49
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.07
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.52
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.04
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.43
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000004753

Normal statistic for number of bits   :   0.038
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.84
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000030073

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    1.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:22.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8683539.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.28
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908013
  j =  2                              :            45992
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908275
  j =  2                              :            45858
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.42
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.09
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.91
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.39
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.98
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12092.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.34
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000005824

Normal statistic for number of bits   :   0.046
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.93
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000220621

Normal statistic for number of bits   :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:02.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9666579.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5304
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:28.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.88
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.27
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908066
  j =  2                              :            45961
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908129
  j =  2                              :            45928
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17337.34
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.71
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.25
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.98
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.74
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.09
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.42
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999810032

Normal statistic for number of bits   :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.45
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000100855

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:55.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10616851.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7063
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.33
p-value of test                       :  6.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.22
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :  104.41
p-value of test                       :  4.7e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.23
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.89
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908205
  j =  2                              :            45896
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908860
  j =  2                              :            45564
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.83
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.21
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.34
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.14
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.49
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.26
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  445.43
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.76
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.03
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.55
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9748.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4649.39
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:43.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.17
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000006853

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.88
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999964010

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:28.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          4.7e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11993107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.94
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.49
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.58
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908637
  j =  2                              :            45677
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907709
  j =  2                              :            46135
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.49
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.99
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.88
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.85
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.52
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.64
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.46
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11442.73
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.67
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999902936

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.98
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999770444

Normal statistic for number of bits   :   -1.81
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:44.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13107219.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:19.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.09
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.21
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908758
  j =  2                              :            45612
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908508
  j =  2                              :            45740
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.19e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.68
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.68
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  211.14
p-value of test                       :  3.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.64
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.64
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.92
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.94
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.88
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.13
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.26
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.01

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.40
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.23
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999897272

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000054028

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:28.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 H (L=1000, r=0)     3.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14057491.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    5.42
p-value of test                       :  1.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     822
p-value of test                       :    0.9956

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   26.07
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.30
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.66
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.66
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908530
  j =  2                              :            45729
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908787
  j =  2                              :            45602
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.46e-5
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.16
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.43
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.96
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.64
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.55
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.86
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.41
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000082396

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.12
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000037144

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15073299.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6796.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.40
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:52.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908995
  j =  2                              :            45492
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908786
  j =  2                              :            45601
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.71
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.42
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.03
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.50
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.54
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.04
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.67
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.29
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -401.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.50
p-value of test                       :    0.9999    *****

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:28.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4596.76
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.17
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999980420

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.93
p-value of test                       :    0.9980


-----------------------------------------------
Total number of bits:  8000040936

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.59
p-value of test                       :  4.8e-3

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:30.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15990803.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    4.37
p-value of test                       :  5.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.50
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.46
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46180
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870180
  j =  1                              :        399907641
  j =  2                              :            46178
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907671
  j =  2                              :            46160
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.73
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.84
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.02
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.85
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.22
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.69
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.92
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.95
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.49
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.32
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.00
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:28.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.95
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000014599

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.42
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000095725

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:46.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16973843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.78
p-value of test                       :  4.6e-4    *****

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.39
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.49
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.42
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:49.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908226
  j =  2                              :            45884
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907615
  j =  2                              :            46191
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.03e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  173.28
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.49
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.90
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.80
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   37.29
p-value of test                       :    0.9999    *****


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.49
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.97
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.50
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.10
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.73
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    2.48
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.88
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999908942

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.58
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999983753

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:39.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17989651.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    3.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    3.69
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:16.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.44
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908544
  j =  2                              :            45725
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908539
  j =  2                              :            45726
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.23
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.54
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.60
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.73
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.02
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.18
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.70
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.47
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.08
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999921335

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.96
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000152284

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:16.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18939923.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1235
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334355
  j =  1                              :        599997530
  j =  2                              :             1235
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.49
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.15
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907663
  j =  2                              :            46161
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.44
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.79
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.68
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.76
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.68
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4785.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.67
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.48
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.97
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.07
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999874871

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.31
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000020578

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:02.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20283411.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.94
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.24
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908572
  j =  2                              :            45708
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908382
  j =  2                              :            45806
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:19.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.46
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.66
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.84
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.04
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.08
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.87
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.63
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.91
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.39
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999996443

Normal statistic for number of bits   :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.54
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000090676

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    3.66
p-value of test                       :  1.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:35.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 229383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  365.71
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:26.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.95
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908309
  j =  2                              :            45841
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908005
  j =  2                              :            45996
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.58e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  106.74
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.38
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.78
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.12
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.50
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.91
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.91
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.34
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.32
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.44
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.57
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999916499

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.00
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000001552

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:39.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1310738.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    3.67
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.22
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907708
  j =  2                              :            46140
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908628
  j =  2                              :            45680
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.20e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.99
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.37
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.30
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  412.08
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.65
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4805.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.07
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.78
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.30
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.75
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999991655

Normal statistic for number of bits   :  -0.066
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.13
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000015463

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:28.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2752530.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5241
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.27
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.50
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.33
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.87
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.29
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908025
  j =  2                              :            45986
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907873
  j =  2                              :            46059
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 8.41e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.05
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.09
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.71
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.51
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.41
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.62
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.63
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.35
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9753.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.53
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999944954

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.39
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000078655

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:02.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3670034.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.68
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908097
  j =  2                              :            45950
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907923
  j =  2                              :            46034
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.67
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17733.88
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  309.94
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.67
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.47
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.12
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.25
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999976949

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.24
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999878150

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:41.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4718610.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7113
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  500.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.88
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.62
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908106
  j =  2                              :            45938
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908015
  j =  2                              :            45988
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :  8.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.71
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.95
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.23
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.36
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.54
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.57
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.26
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.86
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999992123

Normal statistic for number of bits   :  -0.062
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.45
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999851057

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5570578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9956

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.72
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.91
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908395
  j =  2                              :            45801
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45543
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869543
  j =  1                              :        399908915
  j =  2                              :            45541
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 3.82e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.86
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.31
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.39
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.28
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.08
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.91
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.66
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.00
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.30
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999941117

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.32
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999837848

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6455314.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     972
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7227.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.61
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.86
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908160
  j =  2                              :            45911
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907872
  j =  2                              :            46058
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.36
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17585.80
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.44
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.72
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.40
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.25
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.92
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.12
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.91
p-value of test                       :  5.1e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.51
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999933233

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.25
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999783269

Normal statistic for number of bits   :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:54.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7536658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.52
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908404
  j =  2                              :            45795
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908610
  j =  2                              :            45689
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.38e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.8e-3

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17973.18
p-value of test                       :  2.0e-3



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.97
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.46
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.54
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.53
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.47
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  443.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.27
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.14
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.13
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.89
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000057976

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.94
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000157462

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:13.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8585234.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.46
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.07
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908288
  j =  2                              :            45847
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908200
  j =  2                              :            45894
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:28.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.55
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.26
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.50
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.06
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.86
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.78
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.96
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.17
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11530.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.86
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999994487

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.24
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000090109

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.72
p-value of test                       :  3.3e-3

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:52.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 52  SampleProd, t = 24              0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9633810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.04
p-value of test                       :  3.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:22.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.27
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:29.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.70
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4916.15
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45456
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869456
  j =  1                              :        399909093
  j =  2                              :            45446
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908390
  j =  2                              :            45802
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.29
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.15
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.50
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.12
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.22
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.97
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.28
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.33
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.65
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999977723

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.10
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999939635

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:59.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10780690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  507.72
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.07
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.34
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:46.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908402
  j =  2                              :            45796
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908490
  j =  2                              :            45749
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  9.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    7.21
p-value of test                       :  2.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17481.93
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.43
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.30
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.11
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.52
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.94
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.41
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:29.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4308.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.06
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999944789

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.37
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000131221

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:03.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 52  SampleProd, t = 24              2.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11829266.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.77
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.06
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908397
  j =  2                              :            45791
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907907
  j =  2                              :            46045
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.20
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.08
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.82
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.45
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.87
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.60
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.84
p-value of test                       :    0.9977

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.96
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.10
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.61
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.14
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999948053

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.36
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000076105

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.90e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.03
p-value of test                       :    0.9988

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         : 1.58e-3
p-value of test                       :    0.50

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:18.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12910610.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5295
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    4.30
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.17
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.88
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908280
  j =  2                              :            45854
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908538
  j =  2                              :            45725
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.01e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.100
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.95
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.71
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.00
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.71
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.67
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.09
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.75
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12194.74
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.49
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999886331

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.98
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999990653

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14024722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.27
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.63
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1255.91
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.17
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.42
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908639
  j =  2                              :            45670
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908263
  j =  2                              :            45861
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.39
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.28
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   39.36
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.32
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.72
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.39
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.74
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.39
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.34
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.14
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.08
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999945131

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.86
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999936212

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.84
p-value of test                       :  2.3e-3

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.80

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:15.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.2e-4
 36  Gap, r = 0                      0.9998 
 76  RandomWalk1 C (L=1000, r=0)     0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15040530.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.03
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.39
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908137
  j =  2                              :            45924
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908037
  j =  2                              :            45974
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.29
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.98
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.21
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.25
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.50
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.71
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.55
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.18
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.09
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.64
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.61
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:29.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.95
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999993188

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000050449

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.45
p-value of test                       :    0.9928

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:10.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16023570.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    6.25
p-value of test                       :  7.6e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     243
p-value of test                       :    0.9996    *****

Stat. AD (mNP2)                       :    4.60
p-value of test                       :  4.5e-3

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.80
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    3.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.22
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.34
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.20
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908095
  j =  2                              :            45948
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908807
  j =  2                              :            45592
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:28.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17576.10
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.87
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.22
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.11
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.91
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.13
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.64
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.27
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.95
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:28.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.41
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000145654

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.70
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000037753

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:06.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          7.6e-4
 24  ClosePairs NJumps, t = 9        0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17104914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.60
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  165.97
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.24
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46121
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870121
  j =  1                              :        399907762
  j =  2                              :            46113
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908573
  j =  2                              :            45706
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.68e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.44
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.23
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.47
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.57
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  265.99
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.59
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.62
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.49
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999940034

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.07
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000169801

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:48.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18087954.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1517
p-value of test                       :  2.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334637
  j =  1                              :        599996966
  j =  2                              :             1517
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997237
  j =  2                              :             1380
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     353
p-value of test                       :  1.5e-3

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.93
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.23
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46184
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870184
  j =  1                              :        399907637
  j =  2                              :            46174
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908270
  j =  2                              :            45856
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.53
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4770.43
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.99
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.06
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.46
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.19
p-value of test                       :  7.3e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.71
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.86
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.06
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3933.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.86
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999996761

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000063271

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:34.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              0.9998 
  6  CollisionOver, t = 3            2.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19136530.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1241
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334361
  j =  1                              :        599997518
  j =  2                              :             1241
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9971

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.55
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.30
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908565
  j =  2                              :            45713
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908256
  j =  2                              :            45866
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.33
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.49
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.70
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.28
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.19
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4813.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.46
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.87
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-4
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11513.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.15
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999886235

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.59
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000129151

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:42.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20119570.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1494
p-value of test                       :  2.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334614
  j =  1                              :        599997012
  j =  2                              :             1494
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7561
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    4.36
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.96
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.24
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908659
  j =  2                              :            45666
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908105
  j =  2                              :            45943
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9950


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:28.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.82
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.30
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.93
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.22
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.29
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.38
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  468.97
p-value of test                       :  9.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.97
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:35.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.65
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000078436

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000031111

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:49.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           2.8e-4
 79  RandomWalk1 R (L=10000, r=15)   9.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 262152.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:46.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.91
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  507.12
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1555.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6767.08
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.86
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4870.41
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908136
  j =  2                              :            45926
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908366
  j =  2                              :            45811
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.05
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.40
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.28
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.88
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.13
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.84
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.61
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.53
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.55
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.33
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.17
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000030907

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.07
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999957509

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:00.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1867784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1330.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.77
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.13
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908009
  j =  2                              :            45991
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908469
  j =  2                              :            45758
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17057.29
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.88
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.28
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.82
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.88
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.16
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.85
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.99
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.09
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999971780

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.06
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000186217

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2916360.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:28.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.24
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.38
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.32
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907836
  j =  2                              :            46073
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.66
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.19
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.49
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.30
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.13
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.91
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.46
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.38
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.34
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.20
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.19
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5092.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.61
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000007972

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.57
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999858872

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:09.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3866632.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.93
p-value of test                       :  9.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.26
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:28.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.18
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.64
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908365
  j =  2                              :            45813
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908711
  j =  2                              :            45643
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.81e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9939


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.69
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.56
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.05
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.10
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.76
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.20
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.89
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000052456

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.39
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000007255

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:53.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5046280.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4184
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.40
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4869.78
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908474
  j =  2                              :            45757
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908143
  j =  2                              :            45927
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17842.43
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.68
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.01
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.42
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.27
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.40
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.16
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.20
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12095.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.60
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999958487

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.51
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000019093

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:56.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5931016.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.95
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.48
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.84
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46291
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870291
  j =  1                              :        399907421
  j =  2                              :            46285
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907983
  j =  2                              :            46004
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.46
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.19
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5217.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.79
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.77
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.62
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999997877

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.15
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999963107

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6914056.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6792.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908028
  j =  2                              :            45980
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907973
  j =  2                              :            46009
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17040.12
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.83
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.53
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.36
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.49
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.48
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.36
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.27
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.34
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4653.95
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999952346

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.68
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999920771

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.50
p-value of test                       :    0.9938

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:38.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7897096.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.11
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:28.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.34
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908204
  j =  2                              :            45889
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46399
p-value of test                       :  7.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870399
  j =  1                              :        399907207
  j =  2                              :            46389
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.95
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17685.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.44
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.78
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.69
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.22
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.86
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.29
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.85
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.79
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.08
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.49
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999984530

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.67
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999867404

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:45.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8880136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7544
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.50
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:28.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.79
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:54.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908607
  j =  2                              :            45692
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907867
  j =  2                              :            46062
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.09
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.31
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.14
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.56
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.54
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.47
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.08
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.57
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.74
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.57
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000073909

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.81
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000008083

Normal statistic for number of bits   :   0.064
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.32
p-value of test                       :    0.01

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:34.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10059784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.70
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.01
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908257
  j =  2                              :            45870
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17981.96
p-value of test                       :  1.7e-3



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.47
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -401.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.53e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10284.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10253.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.31
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000062152

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.71
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000055462

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    2.51
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:01.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11075592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.95
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7352.77
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:50.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908530
  j =  2                              :            45732
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   69.26
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17132.63
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.05
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.75
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.91
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    2.41
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.81
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4276.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.72
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999913181

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.80
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999977636

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:50.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11960328.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.56
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.97
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:51.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908135
  j =  2                              :            45928
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907682
  j =  2                              :            46153
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.55
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.21
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.59
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.23
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.88
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.57
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000089236

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.67
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000002938

Normal statistic for number of bits   :   0.023
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.19
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:02.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12943368.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.97
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.12
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.56
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:53.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908418
  j =  2                              :            45782
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45600
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869600
  j =  1                              :        399908803
  j =  2                              :            45594
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.46
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.88
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.50
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5234.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.48
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.86
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.16
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:29.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.35
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.16
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.30
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000035428

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.59
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000068104

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.036
p-value of test                       :    0.51

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.013
p-value of test                       :    0.51

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:32.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13762568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.16
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.82
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46266
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870266
  j =  1                              :        399907469
  j =  2                              :            46264
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908793
  j =  2                              :            45599
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9911


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.06
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.72
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.33
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.71
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.82
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.70
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.19
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9706.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.19
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999814256

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.39
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000024475

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:27.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14811144.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     828
p-value of test                       :    0.9920

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.63
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.46
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.48
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.96
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.98
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908820
  j =  2                              :            45584
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907807
  j =  2                              :            46089
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.69
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.51
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.42
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.81
p-value of test                       :  5.0e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10272.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:33.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.95
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000023587

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.67
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999922751

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:40.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               5.0e-4
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15728648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.04
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  491.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.25
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.22
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.00
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908182
  j =  2                              :            45909
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907744
  j =  2                              :            46122
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.46
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.54
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.63
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.51
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.56
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.60
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.65
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.36
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -401.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.28
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999970238

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.11
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000044803

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:49.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16941064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     657
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.68
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  299.54
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.01
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:47.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908139
  j =  2                              :            45929
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.46
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.35
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.11
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.06
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.06
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.39
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:28.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.79
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999904883

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.50
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999885983

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:18.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17956872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.58
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907850
  j =  2                              :            46069
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907909
  j =  2                              :            46035
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-5
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.37
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.53
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.71
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.61
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.48
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.98
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.89
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.80
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.07
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.69
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.95
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.94
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000043882

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.43
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999883052

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    2.87
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:10.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18874376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.81
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9996    *****

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.54
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.00
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907806
  j =  2                              :            46091
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17696.23
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.81
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.55
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.75
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.34
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.27
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.25
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  2.2e-4    *****

Anderson-Darling statistic = A2       :    6.93
p-value of test                       :  3.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10473.03
p-value of test                       :  4.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10220.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.48
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000081931

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.42
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000161872

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:25.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 90  HammingWeight2, r = 0           4.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19890184.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7229.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.79
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.06
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.72
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908637
  j =  2                              :            45680
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908219
  j =  2                              :            45886
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17726.16
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.10
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.63
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.11
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.11
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.87
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -401.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4696.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4344.07
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.56
p-value of test                       :  9.1e-3


-----------------------------------------------
Total number of bits:  8000092278

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.34
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999942725

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:00.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 294921.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.83
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.99
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:48.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908342
  j =  2                              :            45826
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908106
  j =  2                              :            45947
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.59
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.32
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.41
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.27
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.46
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.71
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.50
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.66
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.36
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.34
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.29
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000013060

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.78
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999937412

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:01.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1507337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     185
p-value of test                       :  3.2e-3

Stat. AD (mNP2)                       :    3.89
p-value of test                       :  9.9e-3

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.26
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.73
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908594
  j =  2                              :            45694
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908262
  j =  2                              :            45863
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.02e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.23
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.44
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.01
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.16
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.25
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.72
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.03
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.60
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.12
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.02
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10267.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.92
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999887468

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.54
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000067858

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2392073.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.98
p-value of test                       :  1.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    5.06
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     530
p-value of test                       :    0.9981

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:32.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.65
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4885.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:51.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908255
  j =  2                              :            45868
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46152
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870152
  j =  1                              :        399907698
  j =  2                              :            46148
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.37
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.98
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.02
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.74
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.78
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.36
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.59
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.69
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.11
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.90
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.42
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.67
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.41
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999931679

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.19
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999899024

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:39.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 84  Fourier3, r = 0                 0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3145750.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.21
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.53
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908375
  j =  2                              :            45808
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908032
  j =  2                              :            45981
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.06e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.25
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.95
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.97
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.90
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.17
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.00
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.09
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.15
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.00
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.31
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.60
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000087526

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.25
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000039847

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.12
p-value of test                       :    0.98

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4128790.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9940

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:37.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.47
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  368.01
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.17
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.37
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.96
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907898
  j =  2                              :            46039
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907871
  j =  2                              :            46063
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17548.27
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.96
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.28
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.68
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.06
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.82
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.39
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.76
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.42
p-value of test                       :    0.9918


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.74
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5118.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.51
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999984881

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.21
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999905543

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:51.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5177366.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.66
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.62
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908926
  j =  2                              :            45531
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908277
  j =  2                              :            45854
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17684.85
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.08
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.14
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.89
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.07
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.87
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.76
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.56
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.03
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.01
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10255.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.07
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999918371

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.64
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999923918

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:06.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6225942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.85
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45448
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869448
  j =  1                              :        399909105
  j =  2                              :            45446
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908437
  j =  2                              :            45774
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.12
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17800.16
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.07
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.08
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.76
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.24
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.66
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.8e-3

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:29.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.53
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999879017

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.86
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999937169

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7274518.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5252
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.98
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.99
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4805.69
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908741
  j =  2                              :            45619
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908384
  j =  2                              :            45805
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.24
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.42
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   63.53
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.67
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.28
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.75
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.34
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.22
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.24
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.17
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.47e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.84
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:28.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.56
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999851033

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.01
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000133297

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8224790.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997119
  j =  2                              :             1439
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4156
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45571
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869571
  j =  1                              :        399908861
  j =  2                              :            45565
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908333
  j =  2                              :            45826
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.038
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16930.38
p-value of test                       :    0.9965



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.14
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.28
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.35
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.75
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.50
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10255.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.86
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:03:26.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.08
p-value of test                       :  4.4e-3


-----------------------------------------------
Total number of bits:  7999861413

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.51
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000093817

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:31.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9273366.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    4.04
p-value of test                       :  8.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1542.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6823.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.08
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46156
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870156
  j =  1                              :        399907693
  j =  2                              :            46146
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908530
  j =  2                              :            45726
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-6
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.25
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.36
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.95
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.32
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.88
p-value of test                       :  5.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.47
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.17
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000158962

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   95.23
p-value of test                       :  4.6e-4    *****


-----------------------------------------------
Total number of bits:  8000230722

Normal statistic for number of bits   :    1.82
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 102  Run of bits, r = 27             4.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10256406.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908809
  j =  2                              :            45594
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908680
  j =  2                              :            45654
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.99
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.63
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.50
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.77
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  144.07
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.54
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.74
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.01
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000068026

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.56
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000031897

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         : -6.44e-3
p-value of test                       :    0.50

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:35.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11272214.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9907

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  502.96
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7335.83
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.68
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.47
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.80
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908690
  j =  2                              :            45649
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907666
  j =  2                              :            46161
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  8.6e-4    *****

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:18.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:29.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.67
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.37
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.21
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.76
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.85
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.72
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10352.63
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.87
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999902657

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.81
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999981389

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:20.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12288022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7075
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.67
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.40
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908081
  j =  2                              :            45958
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908048
  j =  2                              :            45967
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.71
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.59
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.13
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.91
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.12
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.72
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.54
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.50
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.49
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.73
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999967058

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.61
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000096424

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:28.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13271062.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9921


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.33
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46361
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870361
  j =  1                              :        399907284
  j =  2                              :            46349
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908745
  j =  2                              :            45620
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.65
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.72
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.24
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.56
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.22
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.07
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12250.73
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.61
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000002398

Normal statistic for number of bits   :   0.019
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.24
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999900179

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:34.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14286870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    4.41
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.14
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908508
  j =  2                              :            45740
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908799
  j =  2                              :            45596
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.27
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.16
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.77
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.38
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.34
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.57
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9695.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.51
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4343.15
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.45
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.70
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999973775

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.27
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999877010

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:16.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15269910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    3.98
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.76
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6734.83
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.06
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908496
  j =  2                              :            45746
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907950
  j =  2                              :            46016
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.09
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.64
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.44
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.88
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.00
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.43
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.38
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.57
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.01
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.13
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.61
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4637.17
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.41
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000079042

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.10
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000075352

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:29.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16285718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5607
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    5.80
p-value of test                       :  1.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     352
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    3.58
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.45
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.16
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907733
  j =  2                              :            46129
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.07
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  587.12
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.06
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.17
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.21
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.51
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.00
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000039427

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000034870

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:29.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17301526.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908233
  j =  2                              :            45876
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908194
  j =  2                              :            45900
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.42e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.20e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17261.05
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.44
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.93
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.72
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.44
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.14
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.70
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.82
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4656.59
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.07
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999963212

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.91
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000130258

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:48.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18317334.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.00
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908398
  j =  2                              :            45792
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908585
  j =  2                              :            45688
  j =  3                              :               13
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   15.39
p-value of test                       :  4.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17427.19
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.52
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.04
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.60
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.86
p-value of test                       :  2.0e-3


-----------------------------------------------
Total number of bits:  8000073201

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.85
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000004582

Normal statistic for number of bits   :   0.036
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:29.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 71  MatrixRank, L=5000              4.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19333142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7114
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.31
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.50
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907775
  j =  2                              :            46108
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908221
  j =  2                              :            45885
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.39
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.17
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.91
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.08
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.22
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.76
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.84
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.85
p-value of test                       :  5.2e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11484.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.36
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999963014

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.48
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000085978

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:17.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 327690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.58
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.17
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46535
p-value of test                       :  1.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870535
  j =  1                              :        399906930
  j =  2                              :            46535
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908011
  j =  2                              :            45990
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17223.70
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.31
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.44
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.95
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.02
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.85
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.86
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999893426

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.62
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999998051

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.8e-3

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         : -4.34e-3
p-value of test                       :    0.50

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:55.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1703946.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5572
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4497
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4478
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.66
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908327
  j =  2                              :            45829
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908123
  j =  2                              :            45931
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9936


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.35
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.96
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.41
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.84
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.13
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.86
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.56
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11469.07
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.77
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000191167

Normal statistic for number of bits   :    1.51
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.18
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999997319

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:56.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2555914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1230
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334350
  j =  1                              :        599997540
  j =  2                              :             1230
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    3.01
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7215.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.25
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908230
  j =  2                              :            45882
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46416
p-value of test                       :  6.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870416
  j =  1                              :        399907170
  j =  2                              :            46412
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.83e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.64
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   52.31
p-value of test                       :  7.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.94
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   88.92
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.93
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.92
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.32
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.41
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.09
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.3e-3

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.51
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5121.05
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   97.94
p-value of test                       :  2.4e-4    *****


-----------------------------------------------
Total number of bits:  7999830423

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.47
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000023797

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:50.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9999 
 74  RandomWalk1 R (L=50, r=0)       7.1e-4
 77  RandomWalk1 R (L=1000, r=20)    0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 101  Run of bits, r = 0              2.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3735562.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.90
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:56.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.77
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908822
  j =  2                              :            45583
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908402
  j =  2                              :            45793
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.34
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.099
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.75
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.85
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.17
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.14
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.70
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.54
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.17
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5143.68
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.45
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999910031

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.95
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000080281

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:52.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4784142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997269
  j =  2                              :             1364
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9996    *****

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.12
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4858.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907990
  j =  2                              :            46002
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907972
  j =  2                              :            46011
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.50
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.28
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.00
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.42
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.35
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.28
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3884.38
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000015913

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   87.03
p-value of test                       :  2.9e-3


-----------------------------------------------
Total number of bits:  7999956714

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:56.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5832718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     973
p-value of test                       :  8.4e-3

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    4.30
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:14.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.98
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.17
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.38
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908773
  j =  2                              :            45612
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908553
  j =  2                              :            45719
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.79
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.16
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.54
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.05
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.25
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.51
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000006025

Normal statistic for number of bits   :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999977597

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:42.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6979598.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:47.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.81
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.12
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908327
  j =  2                              :            45832
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908118
  j =  2                              :            45935
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.56e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17613.82
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.39
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.97
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.23
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.99
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.87
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    4.58
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10376.72
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    5.95
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5217.79
p-value of test                       :  5.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999910670

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.69
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000007945

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:41.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 95  HammingIndep, L=30, r=0         5.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7995406.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.14
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908786
  j =  2                              :            45604
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908026
  j =  2                              :            45984
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.26
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.36
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.75
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.21
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.66
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.40
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.19
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.67
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.02
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.06
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999952067

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.16
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000053767

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:36.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9076750.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    7.00
p-value of test                       :  3.5e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.77
p-value of test                       :  1.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  371.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.07
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.43
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907886
  j =  2                              :            46048
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908130
  j =  2                              :            45929
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.75e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.17
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.40
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.01
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.55
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5195.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.33
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.84
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.32
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.02
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9968

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.84
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.98
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12104.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.61
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000087763

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.75
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999937298

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:35.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           3.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10027022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:47.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.19
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.51
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46291
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870291
  j =  1                              :        399907421
  j =  2                              :            46285
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907919
  j =  2                              :            46039
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  8.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9959


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17551.18
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.03
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.42
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.47
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.83
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999934607

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.72
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999932231

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11042830.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.55
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.95
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908254
  j =  2                              :            45867
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908825
  j =  2                              :            45586
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.74
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.59
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.89
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.17
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.44
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.79
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.99
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.18
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.10
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.42
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000001114

Normal statistic for number of bits   : 8.81e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.36
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000102706

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:50.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12058638.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.94
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.85
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:00.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908920
  j =  2                              :            45525
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908030
  j =  2                              :            45979
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17881.02
p-value of test                       :  8.2e-3



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.84
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.84
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.83
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5201.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.80
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.78
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.61
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:29.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12124.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.37
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000053686

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.96
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999890399

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:12.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12976142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     544
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.86
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.78
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7315.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.07
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.56
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.89
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:53.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907922
  j =  2                              :            46036
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907876
  j =  2                              :            46059
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:28.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.75
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.73
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.13
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.60
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.02
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.07
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    : 1.66e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.48
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.43
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.52
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.72
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999940673

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.36
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000019849

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:11.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13959182.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4490
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    3.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.56
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.98
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907902
  j =  2                              :            46043
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.48
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.28
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.29
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.81
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.67
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.01
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9746.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.25
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999962903

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.27
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000046855

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:25.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14909454.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9977

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4185
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7228.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.91
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.43
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:53.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907784
  j =  2                              :            46108
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17606.70
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.87
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.89
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.09
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.20
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.83
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.18
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.86
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.77
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000033859

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.30
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999874685

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:00.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15892494.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.42
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.71
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908508
  j =  2                              :            45743
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46223
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870223
  j =  1                              :        399907559
  j =  2                              :            46213
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.30
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16980.45
p-value of test                       :    0.9924



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.68
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.63
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.16
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.47
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000178276

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.29
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999746750

Normal statistic for number of bits   :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:21.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16711694.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9906

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:37.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6738.79
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.01
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908708
  j =  2                              :            45643
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908452
  j =  2                              :            45762
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.93e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17587.77
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.68
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.27
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.81
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.55
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.33
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.25
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.48
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.43
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.66
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999976358

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.72
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999921938

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.16

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:36.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17694734.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1236
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334356
  j =  1                              :        599997528
  j =  2                              :             1236
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.12
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.36
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.11
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908427
  j =  2                              :            45782
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908789
  j =  2                              :            45598
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17203.79
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.78
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.82
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.45
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.75
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.79
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.47
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.85
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  140.10
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9658.17
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:28.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.01
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000030217

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.89
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000013501

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:38.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 89  PeriodsInStrings, r = 20        0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18710542.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:26.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:03:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:29.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.91
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907675
  j =  2                              :            46155
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908214
  j =  2                              :            45881
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.59
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.78
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.45
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.79
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.24
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.89
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.21
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.04
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.68
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.41
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000035806

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.17
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000005173

Normal statistic for number of bits   :   0.041
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.11e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:55.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19693582.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    3.24
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.36
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908088
  j =  2                              :            45947
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907891
  j =  2                              :            46053
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.52e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 8.69e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17595.45
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.92
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.60
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.57
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.30
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.98
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.61
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  2.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.26
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11477.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000197449

Normal statistic for number of bits   :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.34
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000065929

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:59.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 360459.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  514.69
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7229.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:52.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46203
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870203
  j =  1                              :        399907599
  j =  2                              :            46193
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907940
  j =  2                              :            46027
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.14e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.53
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.17
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.74
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.20
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.92
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999879962

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.31
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000035101

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    2.41
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:06.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1540107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5596
p-value of test                       :  9.1e-3


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     538
p-value of test                       :    0.9946

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.51
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.23
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.02
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:49.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46337
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870337
  j =  1                              :        399907333
  j =  2                              :            46323
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45427
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869427
  j =  1                              :        399909150
  j =  2                              :            45419
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.79
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.96
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.57
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.07
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.80
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.89
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:35.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.92
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000080185

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.55
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000044059

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:42.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2457611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.75
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4825.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:49.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46279
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870279
  j =  1                              :        399907444
  j =  2                              :            46275
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.63
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.75
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.55
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.95
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.39
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.84
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.35
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.08
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000107674

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.16
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999945326

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:02.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3506187.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    4.01
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1527.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.77
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.46
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399908996
  j =  2                              :            45499
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908611
  j =  2                              :            45693
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.03
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.22
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:28.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.08
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.09
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.85
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.95
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.04
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.69
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.85
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.43
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000032464

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.84
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000151942

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:55.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4423691.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    4.39
p-value of test                       :  5.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :    1013
p-value of test                       :  1.2e-4    *****

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:38.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:32.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.28
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:53.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46289
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870289
  j =  1                              :        399907427
  j =  2                              :            46279
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.44
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.46
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.00
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4767.53
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.35
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.41
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.95
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4306.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.65
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000024064

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.59
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000081559

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:20.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        1.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5275659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6881.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.33
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4878.04
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:56.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907733
  j =  2                              :            46132
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45501
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869501
  j =  1                              :        399909001
  j =  2                              :            45495
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17166.03
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.81
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.21
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.97
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.92
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.46
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.67
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.57
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.39
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000068644

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.05
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999963464

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6357003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7356.84
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.22
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.45
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4819.45
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907687
  j =  2                              :            46155
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.48
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.32
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.03
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.03
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.02
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.20
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.14
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.41
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.02
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.11
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999948071

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000028738

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7307275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5239
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.84
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.85
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4876.42
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908387
  j =  2                              :            45802
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907614
  j =  2                              :            46190
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.15
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.90
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.31
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.77
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.60
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10301.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.83
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999892931

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.35
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000161260

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:42.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8323083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.06
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     816
p-value of test                       :    0.9976

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.77
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.50
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5178.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908435
  j =  2                              :            45778
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907604
  j =  2                              :            46192
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.64
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.40
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.55
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.93
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.95
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.38
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5135.89
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.68
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999889949

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999916826

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:46.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9338891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9957


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9979


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    4.39
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.62
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.13
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:59.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908316
  j =  2                              :            45839
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908619
  j =  2                              :            45689
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.07e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.02e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.29
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.90
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.98
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.47
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.56
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.82
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.03
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.12
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9763.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:30.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.93
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.34
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999984578

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.12
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000084028

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:02.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10387467.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.58
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.18
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908406
  j =  2                              :            45788
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908726
  j =  2                              :            45631
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.96
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.88
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5255.08
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.25
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.21
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.33
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.85
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.74
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11545.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.41
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000146476

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.67
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000096595

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         : -8.70e-3
p-value of test                       :    0.50

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:31.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11403275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.89
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.37
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908174
  j =  2                              :            45904
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908196
  j =  2                              :            45896
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  7.7e-4    *****

Anderson-Darling statistic = A2       :    5.88
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    6.55
p-value of test                       :  5.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17030.60
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.19
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.32
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.33
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.95
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.31
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.63
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.60
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.01
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.07
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.61
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.48
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000007681

Normal statistic for number of bits   :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.73
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999963317

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:44.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              5.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12419083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5627
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.27
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.62
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908828
  j =  2                              :            45580
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46312
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870312
  j =  1                              :        399907379
  j =  2                              :            46306
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.04
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.50
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.95
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.95
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.27
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.22
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.18
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.05
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.43
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :7.02e-17
p-value of test                       :    0.50

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.82
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:26.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5076.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.00
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999991274

Normal statistic for number of bits   :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.07
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999964442

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : -6.00e-4
p-value of test                       :    0.50

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:33.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13434891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7206.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.51
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.13
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908315
  j =  2                              :            45829
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908723
  j =  2                              :            45631
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.14
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.31
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.82
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.88
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.12
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.38
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.63
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.35e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.10
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12112.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.12
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999988514

Normal statistic for number of bits   :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.39
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000094585

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9914

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:44.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14417931.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9990    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.68
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.47
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.34
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46188
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870188
  j =  1                              :        399907627
  j =  2                              :            46182
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45527
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869527
  j =  1                              :        399908950
  j =  2                              :            45519
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.59
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.80
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.33
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.46
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:24.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.66
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000064822

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.23
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000036859

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:20.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15433739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.60
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:29.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.65
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4864.41
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907801
  j =  2                              :            46095
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907787
  j =  2                              :            46096
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:28.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:29.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.51
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.92
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.91
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.01
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:28.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.05
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000018097

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.14
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999985586

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:08.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16449547.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     679
p-value of test                       :  8.3e-4    *****

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.91
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.75
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.92
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908208
  j =  2                              :            45890
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907860
  j =  2                              :            46061
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.96
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.43
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.49
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.72
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.01
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.77
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.74
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.27
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:28.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.13
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999924704

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.56
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999948521

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:52.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs NJumps, t = 5        8.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17465355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5283
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.52
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.79
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.98
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908140
  j =  2                              :            45924
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908744
  j =  2                              :            45622
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.43
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.88
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.70
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.78
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.88
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.33
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.10
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.59
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.00
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000225337

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.97
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999989546

Normal statistic for number of bits   :  -0.083
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:59.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18481163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7063
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    4.57
p-value of test                       :  4.6e-3

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.49
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.97
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:59.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908510
  j =  2                              :            45742
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46343
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870343
  j =  1                              :        399907318
  j =  2                              :            46335
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.64e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17363.15
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.37
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.51
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.62
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.58
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  477.56
p-value of test                       :  7.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.21
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.95
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.14
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.95
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.89
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.56
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999865199

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.55
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999960413

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:42.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   7.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19496971.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.75
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.39
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:00:28.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907854
  j =  2                              :            46073
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908154
  j =  2                              :            45920
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:15.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17458.09
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.97
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.56
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.89
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.55
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.19
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.96
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4652.12
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.51
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999927218

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.61
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999987989

Normal statistic for number of bits   :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:54:10.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 393228.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:48.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.63
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.41
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5312.61
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908195
  j =  2                              :            45892
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908332
  j =  2                              :            45831
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.80
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.08
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.54
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.77
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.12
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.55
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.58
p-value of test                       :    0.9912

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000163615

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.00
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999965624

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:14.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1998860.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4130
p-value of test                       :    0.9992    *****


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.52
p-value of test                       :  5.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9980

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:02:59.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908806
  j =  2                              :            45591
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907589
  j =  2                              :            46195
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.93
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.21
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.44
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.28
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.03
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.60
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5250.14
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.80
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.78
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.84
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.31
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.98
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999821939

Normal statistic for number of bits   :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.23
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000019330

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:27.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3014668.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.72
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    3.99
p-value of test                       :  8.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    4.03
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.22
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4909.38
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908861
  j =  2                              :            45562
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907907
  j =  2                              :            46045
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.98e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:14.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17192.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.38
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.19
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.30
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4648.59
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.01
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999897230

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.15
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999893090

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.20
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:12.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3964940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5277
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.43
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:15.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:50.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.96
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.16
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.87
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.20
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.14
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907984
  j =  2                              :            45999
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908184
  j =  2                              :            45902
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.56e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17427.66
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.59
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.05
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.72
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.45
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.50
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.95
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4331.30
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.04
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999974234

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.13
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999970442

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:46.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4947980.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4505
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.03
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.76
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908938
  j =  2                              :            45528
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907987
  j =  2                              :            46002
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.99
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.94
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.98
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.59
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.12
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4777.48
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.23
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.36
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.70
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.58
p-value of test                       :  6.4e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.76
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.69
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:34.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.89
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999954794

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.84
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000070414

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:28.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5996556.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.73
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4915.53
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908051
  j =  2                              :            45970
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907670
  j =  2                              :            46156
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.33
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.26
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17185.72
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.16
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.75
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.49
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.95
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.15
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.49
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.97
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.98
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.05
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12140.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.53
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999933098

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.19
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999962537

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    2.56
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:29.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6946828.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1493
p-value of test                       :  3.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334613
  j =  1                              :        599997014
  j =  2                              :             1493
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:02:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.22
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.32
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:57.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908362
  j =  2                              :            45816
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908037
  j =  2                              :            45977
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.89e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17710.81
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.16
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.26
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.76
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.45
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.50
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.56
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000047662

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.68
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000061105

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           3.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7962636.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.68
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.21
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908831
  j =  2                              :            45577
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.70
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.91
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.86
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.90
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.29
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9637.73
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.97
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999888917

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.65
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999897467

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:07.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8978444.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9988

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.56
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5247.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:53.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908429
  j =  2                              :            45781
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46086
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870086
  j =  1                              :        399907830
  j =  2                              :            46082
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.68e-6
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.79e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.72
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  168.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17570.37
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.04
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.70
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.01
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.87
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.86
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.18
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.55
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:32.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.36
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999938579

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.30
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999977531

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:14.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9928716.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    4.03
p-value of test                       :  8.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    3.16
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  373.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:29.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45510
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869510
  j =  1                              :        399908985
  j =  2                              :            45500
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908820
  j =  2                              :            45584
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9966


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.47e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17174.94
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   61.98
p-value of test                       :  5.6e-5    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.53
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.29
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.58
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.32
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.56
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.58
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.07
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.47
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.76
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000054961

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.35
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000153403

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:33.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 J (L=50, r=0)       5.6e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10944524.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    4.32
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.97
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.55
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46301
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870301
  j =  1                              :        399907401
  j =  2                              :            46295
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907918
  j =  2                              :            46035
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:10.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.86e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :  1.0e-2

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9983


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.93e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.21
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.09
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   39.52
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.30
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.86
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.93
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.39
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.27
p-value of test                       :  3.6e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    6.17
p-value of test                       :  8.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10401.55
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9768.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.72
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999968792

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.07
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000141049

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:39.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11927564.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6843.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.11
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4958.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908185
  j =  2                              :            45900
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908162
  j =  2                              :            45916
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.67e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.34
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.73
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.52
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.82
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.49
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.83
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.11
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.91
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999914957

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000032491

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:55.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12845068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.07
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6789.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908572
  j =  2                              :            45708
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907768
  j =  2                              :            46110
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.00
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.33
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.93
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.58
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.70
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.78
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10340.86
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5220.28
p-value of test                       :  5.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11539.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.58
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999916352

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000055582

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:17.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 96  HammingIndep, L=30, r=27        5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14123020.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.52
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:47.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907904
  j =  2                              :            46045
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908597
  j =  2                              :            45700
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17094.60
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.26
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.46
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.76
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.52
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.01
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4842.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.38
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.27
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.06
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.06
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.11
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:29.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5101.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4642.00
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11452.02
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999952859

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000081703

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.20
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:41.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15106060.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4620
p-value of test                       :  1.1e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.36
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.89
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:47.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908505
  j =  2                              :            45746
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907548
  j =  2                              :            46220
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.91
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17663.46
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.24
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.53
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.63
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.11
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.46
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.86
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.14
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.51
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.77
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9712.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:33.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.52
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999953375

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.11
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000028501

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:34.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         1.1e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16089100.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5558
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:40.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.25
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908414
  j =  2                              :            45787
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908274
  j =  2                              :            45854
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.37
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  196.22
p-value of test                       :  5.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.82
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.78
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.84
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.47
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.84
p-value of test                       :  2.4e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.35
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999937562

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.13
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999942377

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:42.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 R (L=1000, r=0)     5.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17072140.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.97
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.97
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908664
  j =  2                              :            45662
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.93e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.98
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17052.10
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.59
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.62
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.04
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.73
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.12
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.57
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  151.85
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:28.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.49
p-value of test                       :    0.9983


-----------------------------------------------
Total number of bits:  8000081121

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.34
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999989945

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:07.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18055180.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1555.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.10
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.84
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907646
  j =  2                              :            46174
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907860
  j =  2                              :            46067
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17662.32
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.15
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.95
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.35
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.43
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.88
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.13
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.59
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9675.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12146.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   95.47
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
Total number of bits:  8000088249

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999943064

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:27.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 101  Run of bits, r = 0              4.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18972684.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    5.17
p-value of test                       :  2.4e-3

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1296.89
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.36
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.97
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.22
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907964
  j =  2                              :            46015
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908395
  j =  2                              :            45792
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    5.66
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9990    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.39
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.56
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.19
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.62
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.24
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.43
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.55
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.26
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.71
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.27
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.61
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.30
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999974363

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.95
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999983738

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:36.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19922956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.53
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.53
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.49
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908580
  j =  2                              :            45704
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.54e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.20
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.85
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.80
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.95
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.77
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.92
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.60
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000034015

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.93
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999872522

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:27.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 425997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     111
p-value of test                       :    0.9995    *****

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1575.70
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7205.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:51.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908107
  j =  2                              :            45939
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908259
  j =  2                              :            45866
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.49
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.04
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.00
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.44
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.54
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.41
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.67
p-value of test                       :  3.8e-3

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.65
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999969203

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.81
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000079957

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:11.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1015821.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.15
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.15
p-value of test                       :    0.9984

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.24
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:51.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908429
  j =  2                              :            45778
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908822
  j =  2                              :            45586
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.89
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.55
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.31
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.90
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.44
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.28
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.88
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.07
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.90
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.06
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.29
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999920543

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.85
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000122305

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:17.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2031629.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.22
p-value of test                       :  7.5e-3

Test on the Nm values of W_{n,i}(mNP1):    3.89
p-value of test                       :  9.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.93
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5211.84
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:55.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907826
  j =  2                              :            46081
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9909


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.43
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.00
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.56
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.21
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.27
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  299.64
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.20
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.98
p-value of test                       :    0.9984

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.32
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000072499

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.21
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999893531

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:19.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3047437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5252.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:55.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908239
  j =  2                              :            45873
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907944
  j =  2                              :            46025
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.19e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17028.41
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.65
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.83
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5198.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.11
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.54
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.14
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.61
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.14
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999982982

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000010480

Normal statistic for number of bits   :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:49.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4161549.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.31
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908418
  j =  2                              :            45782
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908336
  j =  2                              :            45826
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:19.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.51e-4
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17039.50
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.71
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.56
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.93
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.51
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5260.20
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.02
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.27
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.36
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3858.96
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.54
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000171790

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.30
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000013768

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:10.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 M (L=10000, r=0)    0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5111821.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.49
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.11
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.02
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908020
  j =  2                              :            45987
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46359
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870359
  j =  1                              :        399907285
  j =  2                              :            46353
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.88e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17068.50
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.42
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.95
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.98
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.92
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:29.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11604.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.74
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.49
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000133450

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000147121

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:55.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6127629.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908537
  j =  2                              :            45730
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907949
  j =  2                              :            46024
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.30
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   68.38
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.00
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.44
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.24
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.11
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.79
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.57
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.48
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:27.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.27
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.56
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999965822

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000159934

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:11.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7143437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9926

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.98
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    3.42
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.58
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908244
  j =  2                              :            45875
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908181
  j =  2                              :            45902
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.53
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.82
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.87
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.16
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.56
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.42
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4741.92
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.57
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.59
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.73
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.85
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.77
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000000895

Normal statistic for number of bits   : 7.08e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.86
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999953324

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:54.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8159245.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.49
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.90
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908136
  j =  2                              :            45932
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908260
  j =  2                              :            45858
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:18.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:12.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17708.08
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.39
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.71
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.01
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.85
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  308.24
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.36
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.50
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.08
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4702.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.17
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000099343

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.36
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000039490

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:10.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9175053.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1515
p-value of test                       :  3.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334635
  j =  1                              :        599996970
  j =  2                              :             1515
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.90
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908731
  j =  2                              :            45627
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908840
  j =  2                              :            45574
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.62e-4
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.79
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.87
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.59
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.59
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.74
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.10
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.65
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.37
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.50
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.05
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000078418

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.74
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000123481

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.63
p-value of test                       :  4.3e-3

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:07.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           3.2e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10190861.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    3.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.74
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4912.30
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907968
  j =  2                              :            46013
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908356
  j =  2                              :            45819
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:28.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:29.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.50
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.04
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.37
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.74
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.79
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.75
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.56
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.36
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.55
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.00
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:28.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.75
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999914438

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.73
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000089206

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:02.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11206669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.25
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6833.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.66
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.23
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45485
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869485
  j =  1                              :        399909032
  j =  2                              :            45481
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46317
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870317
  j =  1                              :        399907370
  j =  2                              :            46309
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.29
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.37
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.83
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.02
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.32
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.35
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999992687

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.81
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000019303

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:26.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12222477.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4180
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.86
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.50
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908546
  j =  2                              :            45727
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907850
  j =  2                              :            46075
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.08
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.30
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.55
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.66
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.85
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.07
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.05
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.51
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3910.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.72
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999995483

Normal statistic for number of bits   :  -0.036
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.02
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999994712

Normal statistic for number of bits   :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:11.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13238285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5593
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:55.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    4.88
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.19
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.55
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908438
  j =  2                              :            45778
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908315
  j =  2                              :            45838
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.02
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.68
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.64
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.90
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.01
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.64
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -401.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.53
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.59
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4415.00
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.59
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000059611

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.08
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000074068

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:42.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 98  HammingIndep, L=300, r=26       6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14254093.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.95
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.56
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907921
  j =  2                              :            46035
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45627
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869627
  j =  1                              :        399908749
  j =  2                              :            45621
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:29.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.65
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.00
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.39
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.69
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.43
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5201.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.15
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.61
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.71
p-value of test                       :  3.4e-3

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.07
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000052096

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.58
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000125698

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:37.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15335437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9947

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.93
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.23
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.63
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907994
  j =  2                              :            46000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908197
  j =  2                              :            45897
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.39
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.52
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.49
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.66
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.65
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.75
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.97
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999916307

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.20
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000062356

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:22.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16318477.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.25
p-value of test                       :  6.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.00
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6953.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.42
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.33
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908678
  j =  2                              :            45655
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908479
  j =  2                              :            45756
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.86
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.00
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.87
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.71
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.94
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.41
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.22
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999880232

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.64
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999942218

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.78
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:56.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17334285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4856.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908300
  j =  2                              :            45841
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908161
  j =  2                              :            45912
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:10.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.49
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.77
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.57
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.09
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.46
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.03
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10242.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.75
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999934364

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.35
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000127516

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:05.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18350093.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.25
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.77
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908289
  j =  2                              :            45854
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908570
  j =  2                              :            45709
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.82
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.33
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.05
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.31
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.28
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.61
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.30
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  144.68
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.68
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.14
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.93
p-value of test                       :  5.0e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11548.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.17
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000010807

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.50
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000129538

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:23.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19365901.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6826.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.92
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.10
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:53.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908302
  j =  2                              :            45843
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908594
  j =  2                              :            45700
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.29
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.22
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.68
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.86
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.97
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.86
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.76
p-value of test                       :    0.9971

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.25
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.47
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10331.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12130.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.03
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000059161

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.02
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999871094

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 458766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997230
  j =  2                              :             1382
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.37
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5244.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:20.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908078
  j =  2                              :            45955
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907877
  j =  2                              :            46060
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.63e-6
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.14
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.57
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.50
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.94
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.37
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.47
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999960515

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.72
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000036376

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:49.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1212430.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :  101.81
p-value of test                       :  9.1e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.11
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.96
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907739
  j =  2                              :            46129
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.04
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.46
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.57
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.19
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.04
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.92
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.24
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.98
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.63
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.33
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.71
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.54
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.67
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.74
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999977096

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999917486

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:51.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9991 
 32  CouponCollector, r = 20         9.1e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2785294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5235
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.16
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:38.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  369.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.21
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.71
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.01
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908346
  j =  2                              :            45818
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46176
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870176
  j =  1                              :        399907650
  j =  2                              :            46172
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.75
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.26
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.81
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11499.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.79
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000048319

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.20
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000090592

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:50.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3768334.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5192
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7093
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.97
p-value of test                       :  9.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:59.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907481
  j =  2                              :            46258
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17898.05
p-value of test                       :  6.4e-3



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.34
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.87
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.14
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.39
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.22
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.89
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.81
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10292.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10298.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.21
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12290.95
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.00
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000005743

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.08
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999962198

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:44.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4751370.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.38
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.89
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45409
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869409
  j =  1                              :        399909184
  j =  2                              :            45405
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908732
  j =  2                              :            45634
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.93
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.30
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.17
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.90
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.46
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.80
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.91
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.92
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.90
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.02
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.65
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999952349

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.50
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000058930

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:59.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5636106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.19
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.80
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.47
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45256
p-value of test                       :    0.9982


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869256
  j =  1                              :        399909494
  j =  2                              :            45244
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908073
  j =  2                              :            45959
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  1.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    6.71
p-value of test                       :  4.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
p-value of test                       : 1 -  5.6e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.56
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.18
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.81
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.06
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.14
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.40
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.30
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.22
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4709.35
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.88
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.06
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -401.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.60
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    6.25
p-value of test                       :  8.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.67
p-value of test                       :    0.9999    *****

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.30
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.23
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999921395

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.43
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999816950

Normal statistic for number of bits   :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:04.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               4.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 82  LempelZiv, r = 0                0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6520842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7078
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4168
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    4.10
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1317.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6878.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.29
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.48
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.56
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908218
  j =  2                              :            45882
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908073
  j =  2                              :            45956
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.62
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.49
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.46
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.98
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.59
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.85
p-value of test                       :  2.1e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5101.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.05
p-value of test                       :  8.2e-3


-----------------------------------------------
Total number of bits:  8000170143

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.93
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000171310

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:05.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7766026.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.84
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.27
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.66
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908120
  j =  2                              :            45937
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908059
  j =  2                              :            45960
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.83
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.31
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.92
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.42
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.51
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.29
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.23
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.49
p-value of test                       :    0.9909


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12187.44
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.13
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000001645

Normal statistic for number of bits   :   0.013
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.29
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999896159

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8847370.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.72
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.80
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907808
  j =  2                              :            46090
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907992
  j =  2                              :            45998
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.74
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.09
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.20
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.96
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.32
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.98
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-4
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999983894

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.12
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999995759

Normal statistic for number of bits   :  -0.034
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9967

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:09.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9863178.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    4.19
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.37
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.06
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.58
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908062
  j =  2                              :            45963
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908003
  j =  2                              :            45991
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-4
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.66e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    6.54
p-value of test                       :  5.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.49
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.74
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.72
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  212.74
p-value of test                       :  2.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.09
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.88
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.65
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.17
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.01
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.59
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -401.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -9.32e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.62
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4302.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.83
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999916592

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.67
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000069292

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:54.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              5.6e-4
 76  RandomWalk1 H (L=1000, r=0)     2.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10846218.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.05
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.92
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.64
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908754
  j =  2                              :            45620
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46318
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870318
  j =  1                              :        399907369
  j =  2                              :            46308
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.06e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.46
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.80
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.12
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.35
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000031675

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.50
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000016798

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:59.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11894794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1328.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7307.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.81
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908620
  j =  2                              :            45681
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907689
  j =  2                              :            46151
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.90
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.20
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.38
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.97
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  197.90
p-value of test                       :  4.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.35
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.16
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:28.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.40
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5173.03
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.19
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000078643

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.58
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999986084

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:46.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    4.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12877834.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7526
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9930


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.96
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907612
  j =  2                              :            46191
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907648
  j =  2                              :            46170
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.56
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.05
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.20
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.19
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.22
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.75
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.30
p-value of test                       :  9.7e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.33
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.99
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999827969

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.70
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000196183

Normal statistic for number of bits   :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:59.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13828117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.55
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.01
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908664
  j =  2                              :            45662
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908613
  j =  2                              :            45686
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.08
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.51
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.22
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.26
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.91
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.25
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.21
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.63
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.25
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10213.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11531.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.34
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000040444

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.90
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999985010

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:32.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14942229.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.08
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.95
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:48.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908683
  j =  2                              :            45651
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908773
  j =  2                              :            45609
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.73
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.85
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.00
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.10
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5319.99
p-value of test                       :  8.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.61
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.12
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.37
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9727.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:28.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.96
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000048550

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.85
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000088267

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:40.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 J (L=10000, r=15)   8.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15663125.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:51.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.00
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:53.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908072
  j =  2                              :            45955
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907797
  j =  2                              :            46100
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9901


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.76
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.20
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   49.46
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.28
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.01
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.93
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.29
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.56
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:29.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.34
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000079624

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999997847

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:09.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16678933.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5587
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  499.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1339.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.46
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:53.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908661
  j =  2                              :            45668
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908806
  j =  2                              :            45591
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.24e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.06
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.22
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.89
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.87
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.22
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.69
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.23
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.82
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.17
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000082195

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.13
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000043183

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.058
p-value of test                       :    0.52

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:25.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17727509.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.31
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.95
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.53
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:48.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908124
  j =  2                              :            45932
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908460
  j =  2                              :            45767
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.70
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  173.61
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17204.08
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.94
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.80
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.10
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.87
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.43
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.36
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.08
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.27
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:27.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12090.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.23
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999945098

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.46
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999909134

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.19
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:11.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18743317.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997221
  j =  2                              :             1388
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.06
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.49
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:53.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908154
  j =  2                              :            45917
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908081
  j =  2                              :            45949
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.30
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.34
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.95
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.97
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.24
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.35
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.65
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.89
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.04
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.95
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999969047

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.64
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999873932

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:51.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19726357.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6877.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5287.81
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908613
  j =  2                              :            45692
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45603
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869603
  j =  1                              :        399908795
  j =  2                              :            45601
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.16e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17597.75
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.64
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.29
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.00
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.63
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.80
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.33
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.31e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.15
p-value of test                       :  4.6e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.96
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999990059

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.40
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999979073

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   0.032
p-value of test                       :    0.49

Sample variance                       :    2.55
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:27.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 491535.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6865.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.38
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.90
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.85
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:50.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907730
  j =  2                              :            46126
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.93
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.100
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.21
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   46.53
p-value of test                       :  1.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.61
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.78
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   93.56
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.83
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.44
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.87
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.61
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.37
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.41
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   90.01
p-value of test                       :  1.5e-3


-----------------------------------------------
Total number of bits:  7999975587

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.65
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999895241

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:38.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      1.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1245191.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.16
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.31
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:48.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907968
  j =  2                              :            46010
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908374
  j =  2                              :            45807
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.45e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.78
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.28
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.56
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.15
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.90
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.18
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.41
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000014248

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.36
p-value of test                       :  9.5e-3


-----------------------------------------------
Total number of bits:  8000194530

Normal statistic for number of bits   :    1.54
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:15.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2490375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9933

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.15
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.74
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:52.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908065
  j =  2                              :            45957
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907879
  j =  2                              :            46053
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17769.21
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   70.40
p-value of test                       :  5.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.96
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.81
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.15
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.06
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.72
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9968

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4347.33
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12048.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12090.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.61
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999868889

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.70
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000124411

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:17.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       5.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3637255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    4.34
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.01
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5192.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908455
  j =  2                              :            45765
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908530
  j =  2                              :            45732
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -9.64e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.81
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.62
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.04
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.71
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.53
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.07
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.13
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.28
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.69
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.40
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000087490

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999934964

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:14.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4685831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.95
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9967

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.71
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.38
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.78
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908576
  j =  2                              :            45712
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908038
  j =  2                              :            45981
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.27
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.96
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.48
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.66
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.58
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.71
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5199.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.92
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.68
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.46
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.24
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000154021

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.12
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999947267

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:46.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5701639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.57
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.53
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:56.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907893
  j =  2                              :            46049
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908873
  j =  2                              :            45559
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.01e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.11
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17144.43
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.99
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.71
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.64
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.90
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.24
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.66
p-value of test                       :  3.9e-3

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999908129

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.22
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999964943

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:49.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6750215.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     967
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.32
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7293.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.67
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.51
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907737
  j =  2                              :            46121
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907987
  j =  2                              :            46005
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.48e-4
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17709.18
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.64
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.67
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.57
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.40
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.82
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.19
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.18
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.80
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.37
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000102220

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.31
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000055675

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.23
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:23.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7634951.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.54
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.30
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.08
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908238
  j =  2                              :            45878
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908541
  j =  2                              :            45728
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.47
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:28.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.82
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.27
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.02
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.43
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.88
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.72
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.54
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5054.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5104.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000000181

Normal statistic for number of bits   : 1.43e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.77
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999867230

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:18.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8716295.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  515.16
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.48
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:58.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908819
  j =  2                              :            45589
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908279
  j =  2                              :            45853
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17902.13
p-value of test                       :  6.0e-3



-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.18
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.59
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.73
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.81
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.93
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.98
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.61
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.03
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000033967

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.39
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999897962

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9830407.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9906

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1327.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.58
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.58
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.29
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907737
  j =  2                              :            46130
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908563
  j =  2                              :            45708
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17785.08
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.08
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.67
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.44
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.85
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000057775

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.78
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999855215

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:44.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10878983.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:20.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.99
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.94
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46255
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870255
  j =  1                              :        399907495
  j =  2                              :            46245
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907655
  j =  2                              :            46168
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.84e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.40
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.34
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.97
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.13
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.18
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.58
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.30
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.84
p-value of test                       :  3.0e-3


-----------------------------------------------
Total number of bits:  8000071353

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.76
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999925379

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:21.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11796487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4154
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.36
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6844.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.36
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908464
  j =  2                              :            45759
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908397
  j =  2                              :            45794
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.58
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17188.43
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.67
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.70
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.41
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.24
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.16
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.98
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999958370

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.85
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999939587

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.66
p-value of test                       :  4.8e-5    *****

Anderson-Darling statistic = A2       :    5.43
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.68
p-value of test                       :  3.7e-3

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.091
p-value of test                       :    0.54

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:43.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12779527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  174.11
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.36
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908083
  j =  2                              :            45954
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907991
  j =  2                              :            46003
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 3.71e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.70
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.75
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.50
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.95
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.10
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.38
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.94
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.47
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.44
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.17
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.24
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11617.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.63
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000134056

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.42
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000021490

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:30.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13893639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5562
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     963
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.89
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:29.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.88
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.16
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908689
  j =  2                              :            45651
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908478
  j =  2                              :            45752
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17083.57
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.83
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.75
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.20
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.49
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    2.47
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.70
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.22
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999820013

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.18
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000017656

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:06.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14876679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    3.49
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     979
p-value of test                       :  4.9e-3

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6755.21
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.28
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907620
  j =  2                              :            46187
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908371
  j =  2                              :            45813
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.35
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.76
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.55
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.10
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.81
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.71
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.42
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.96
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  476.38
p-value of test                       :  9.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.96
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.43
p-value of test                       :  7.6e-3

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.96e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:29.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.46
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.81
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000007936

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.18
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000037744

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         : 2.78e-3
p-value of test                       :    0.50

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:17.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   9.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16056327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    4.95
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.46
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.21
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908510
  j =  2                              :            45739
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908779
  j =  2                              :            45603
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.75e-4
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17536.00
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.85
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.16
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.36
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.46
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.39
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.17
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -403.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:33.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.47
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999985793

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.51
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999952625

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.047
p-value of test                       :    0.48

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.023
p-value of test                       :    0.49

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:53.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17006599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     660
p-value of test                       :  8.3e-3

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4861.44
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46236
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870236
  j =  1                              :        399907530
  j =  2                              :            46232
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.77
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.17
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.33
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.70
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.51
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.79
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.23
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.94
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.52
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:28.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999933536

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.72
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999851321

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:36.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18022407.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5584
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6805.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907886
  j =  2                              :            46051
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908475
  j =  2                              :            45761
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    5.89
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   15.96
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.82
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.92
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.22
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.45
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.58
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.68
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.92
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.87
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:29.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.09
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000086857

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000003724

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:34.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19038215.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997325
  j =  2                              :             1336
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5551
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.01
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908717
  j =  2                              :            45640
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46274
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870274
  j =  1                              :        399907458
  j =  2                              :            46262
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.68
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9958


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.44
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.39
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.38
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.18
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.69
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.75
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.17
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4423.65
p-value of test                       :  4.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11550.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.90
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999921866

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.37
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999758426

Normal statistic for number of bits   :   -1.91
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:43.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 98  HammingIndep, L=300, r=26       4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19988487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1555.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6857.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.13
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908509
  j =  2                              :            45744
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908704
  j =  2                              :            45639
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.78
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.80
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.16
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.34
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.98
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.45
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4760.40
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.13
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.64
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.05e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-4
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.59
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:30.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.69
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000080128

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.74
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999962129

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    3.92
p-value of test                       :  5.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:46.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 524304.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.97
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.34
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.20
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.28
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.93
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.30
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:53.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908187
  j =  2                              :            45899
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907929
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.70
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.01e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.78
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.02
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.94
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.90
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.46
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.65
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.92
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.15
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3879.10
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.63
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999853019

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.48
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999962222

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:17.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1048592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997259
  j =  2                              :             1369
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.18
p-value of test                       :  2.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7253.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907915
  j =  2                              :            46035
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46152
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870152
  j =  1                              :        399907701
  j =  2                              :            46142
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.52e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.90
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.38
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.98
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.39
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.17
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.34
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.20
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.16
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  253.87
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.80
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999979310

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.31
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999957131

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:17.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2097168.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:31.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.21
p-value of test                       :  2.3e-3

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7246.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.47
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908582
  j =  2                              :            45706
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908324
  j =  2                              :            45835
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.29e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.66
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.93
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.63
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.10
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.58
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4851.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.53e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9661.95
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5105.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.92
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999941315

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.71
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000060793

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:30.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3178512.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7576
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    3.17
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:32.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.85
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.90
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908139
  j =  2                              :            45917
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9929


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.01
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.40
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.30
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.20
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.02
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.85
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.82
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.86
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12192.71
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.15
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000018700

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.00
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000022060

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:29.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27                0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4096016.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1517
p-value of test                       :  2.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334637
  j =  1                              :        599996966
  j =  2                              :             1517
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.37
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.21
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908116
  j =  2                              :            45942
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908301
  j =  2                              :            45848
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.30e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.37e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.72
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.34
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.52
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.61
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.01
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.25
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  311.56
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.58
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.54
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999872444

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.39
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000088402

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           2.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5144592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    4.06
p-value of test                       :  8.1e-3

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1314.74
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.02
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908272
  j =  2                              :            45858
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908589
  j =  2                              :            45698
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.38e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  1.0e-2

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.78
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.76
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.12
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.57
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.19
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.85
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.16
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.12
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999933239

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.03
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000123670

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.1e-3

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:26.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6160400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.06
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6890.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:28.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5305.57
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908072
  j =  2                              :            45961
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908669
  j =  2                              :            45658
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.82
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.91
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.86
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.20
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.34
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:29.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12094.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999921017

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.63
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000116335

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:31.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7208976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:37.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.18
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.07
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  515.43
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   97.30
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.28
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4860.69
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46211
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870211
  j =  1                              :        399907582
  j =  2                              :            46203
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907994
  j =  2                              :            46000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.66e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17706.83
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.39
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.44
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.88
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5249.38
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.76
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.60
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.53
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.04
p-value of test                       :    0.9980

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.26
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.93
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000032491

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.93
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999748109

Normal statistic for number of bits   :   -1.99
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8257552.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5303
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.99
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:59.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908150
  j =  2                              :            45922
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908270
  j =  2                              :            45862
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17206.60
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.22
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.40
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.41
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.04
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.02
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.37
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.92
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.16
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:30.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.60
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000032365

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.62
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999969563

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:39.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9240592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5573
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908084
  j =  2                              :            45955
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907983
  j =  2                              :            46004
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.47
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.090
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.49
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  585.44
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.42
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.25
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.61
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.82
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.36
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.15
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.13
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.91
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:29.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5036.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.32
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999971000

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.14
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000098878

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:03.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10289168.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   26.74
p-value of test                       :  3.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7276.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.26
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908166
  j =  2                              :            45914
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908534
  j =  2                              :            45724
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.81
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.32
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.28
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.40
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.82
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.71
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.29
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.88
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.16
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.54
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:28.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.59
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000140098

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000014938

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:15.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                3.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11304976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7241.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.44
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.93
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908019
  j =  2                              :            45983
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907950
  j =  2                              :            46019
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.97
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.90
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.43
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.00
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.93
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.51
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:27.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.78
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000018622

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.87
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999998033

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:49.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12320784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7104
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:02:56.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.69
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.91
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.71
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.31
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:54.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908691
  j =  2                              :            45653
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45442
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869442
  j =  1                              :        399909118
  j =  2                              :            45438
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:28.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.70
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.02
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.64
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.29
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.81
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.73
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.63
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.38
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.34
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.32
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.63
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.27
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000057841

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.29
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999931739

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         : -3.58e-3
p-value of test                       :    0.50

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:28.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13336592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1245
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334365
  j =  1                              :        599997510
  j =  2                              :             1245
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:29.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.65
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908193
  j =  2                              :            45899
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908196
  j =  2                              :            45899
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:28.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.89
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.60
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.97
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.59
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.69
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  189.56
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.22
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  463.25
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.95
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.91
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10278.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:28.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.97
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000084499

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.91
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000002011

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:41.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14352400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:35.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9932

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.24
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.00
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908264
  j =  2                              :            45865
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908397
  j =  2                              :            45797
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.09e-6
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.45
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.86
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5227.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.69
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.07
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4334.57
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12041.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.26
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000297904

Normal statistic for number of bits   :    2.36
p-value of test                       :  9.3e-3



-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.23
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000078277

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:30.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15368208.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997135
  j =  2                              :             1431
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.51
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:29.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.78
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908210
  j =  2                              :            45895
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907863
  j =  2                              :            46064
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.06
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17223.40
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.36
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.86
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.16
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.58
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.21
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.86
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.55
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.28
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.64
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.16
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -6.90e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.97
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999995288

Normal statistic for number of bits   :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.80
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999971684

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:31.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16351248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.13
p-value of test                       :    0.9996    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  168.82
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.18
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46203
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870203
  j =  1                              :        399907597
  j =  2                              :            46197
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.50
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.08
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.43
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.28
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.10
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.44
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.91
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.46
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.06
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.09
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.92
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3946.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.18
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999994922

Normal statistic for number of bits   :  -0.040
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.77
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999924713

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:32.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17367056.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.22
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.34
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:01.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908486
  j =  2                              :            45751
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908179
  j =  2                              :            45906
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.97
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.38
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.34
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.42
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.01
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.38
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.86
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.49
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.45
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.40
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000048814

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.92
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000130093

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:58.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18382864.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1243
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334363
  j =  1                              :        599997514
  j =  2                              :             1243
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.64
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.98
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908437
  j =  2                              :            45774
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908552
  j =  2                              :            45715
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.62
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.62
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.02
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.90
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -403.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10428.28
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4710.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.07
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999890192

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.12
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000088132

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.45e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    6.72
p-value of test                       :  4.9e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.83
p-value of test                       : 1 -  6.5e-5    *****

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:53.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27             1 -  6.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19398672.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:26.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:54.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46226
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870226
  j =  1                              :        399907551
  j =  2                              :            46220
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908322
  j =  2                              :            45836
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.42
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.78
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.17
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.20
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.19
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.18
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.27
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.63
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:03:30.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.92
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000180709

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.89
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000060979

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:42.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 557073.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907929
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908795
  j =  2                              :            45592
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.10e-6
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17296.18
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.14
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.45
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.91
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.07
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.39
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.90
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.31
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.59
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000002203

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.47
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999910028

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:34.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1376273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     967
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  289.08
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6877.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.65
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907537
  j =  2                              :            46227
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45493
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869493
  j =  1                              :        399909017
  j =  2                              :            45487
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.78
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.77
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.83
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.27
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.49
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.05
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.72
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.09
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.03
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.48
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000053995

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.42
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999975236

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:58.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2850833.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7091
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.38
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  297.69
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  502.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1329.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.44
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908210
  j =  2                              :            45892
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907942
  j =  2                              :            46023
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.02e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.68
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.01
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.03
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  599.79
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.39
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.59
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.67
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.15
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000098764

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.31
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000078667

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:00.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3833873.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    6.55
p-value of test                       :  5.5e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    3.09
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.92
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907866
  j =  2                              :            46058
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908178
  j =  2                              :            45902
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.11
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.91
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.65
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.38
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.06e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.13
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9733.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.00
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.64
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000025561

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999893597

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:34.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          5.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4882449.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    3.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.93
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1309.06
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7217.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.05
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908660
  j =  2                              :            45655
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908589
  j =  2                              :            45698
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.30
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.14
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.29
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.05
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.21
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.18
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.85
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.94
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.12
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.08
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999987650

Normal statistic for number of bits   :  -0.098
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.27
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000156685

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:37.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27                0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5799953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.87
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4876.82
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908235
  j =  2                              :            45881
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908182
  j =  2                              :            45906
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17232.35
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.98
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.09
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.12
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.23
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.31
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.12
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.06
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.83
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12114.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.87
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000012952

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.24
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000021673

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:21.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6717457.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.91
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.42
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.31
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45465
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869465
  j =  1                              :        399909072
  j =  2                              :            45461
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908333
  j =  2                              :            45829
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.87
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.77
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.72
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.64
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.75
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11447.84
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.85
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999939218

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000000874

Normal statistic for number of bits   : 6.91e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:22.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7569425.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.75
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.38
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.42
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.98
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:07.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908986
  j =  2                              :            45504
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17524.41
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.64
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.69
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.40
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.19
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.02
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.62
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.18
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999822785

Normal statistic for number of bits   :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   87.17
p-value of test                       :  2.8e-3


-----------------------------------------------
Total number of bits:  8000048184

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:47.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8552465.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6882.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.37
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.19
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908217
  j =  2                              :            45884
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908102
  j =  2                              :            45943
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.77
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.99
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.28
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.74
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.40
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10254.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10274.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.88
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000020542

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.93
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999887159

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:26.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9699345.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    5.44
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:57.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908655
  j =  2                              :            45671
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908296
  j =  2                              :            45852
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.50
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.65
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.43
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.88
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.94
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.05
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.30
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.16
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000089698

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.99
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000051385

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.53
p-value of test                       :  5.7e-3

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:31.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10715153.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997265
  j =  2                              :             1366
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    3.84
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     347
p-value of test                       :  4.3e-3

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.85
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907964
  j =  2                              :            46015
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907541
  j =  2                              :            46225
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.01
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.10
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.12
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.36
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  622.65
p-value of test                       :  1.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.19
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.20
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.56
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.78
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.88
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999934151

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.08
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000013885

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:20.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    1.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11665425.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  349.27
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.33
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.13
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908921
  j =  2                              :            45538
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908165
  j =  2                              :            45910
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.03
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.16
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.59
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.25
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.68
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.02
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.13
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.89
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.95
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.23
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.13
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.53
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.49
p-value of test                       :    0.9929

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.69
p-value of test                       :  1.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5112.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.90
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999895616

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.93
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000123892

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:18.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 92  HammingCorr, L = 30             1.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12582929.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9914

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.09
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.73
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.34
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.92
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:53.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908302
  j =  2                              :            45846
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.86
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.75
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.22
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.62
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.57
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.84
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.73
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.09
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.06
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999929783

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.50
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999871850

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13697041.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4589
p-value of test                       :  7.6e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     352
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1544.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7228.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.65
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.23
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.10
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908448
  j =  2                              :            45770
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17711.99
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.97
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.25
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.14
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.36
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.54
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.42
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.71
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.48
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.99
p-value of test                       :    0.9956


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.13
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.69
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:29.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11463.93
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.09
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000053893

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.75
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000059260

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:49.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         7.6e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15007761.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.22
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.87
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.54
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.45
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908333
  j =  2                              :            45826
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907922
  j =  2                              :            46039
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-6
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    : 4.15e-4
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    6.28
p-value of test                       :  7.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.68
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.84
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.06
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.89
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.81
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.94
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 4.88e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:28.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.1e-4    *****

Anderson-Darling statistic = A2       :    5.71
p-value of test                       :  1.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5193.63
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.16
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.47
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999999428

Normal statistic for number of bits   : -4.52e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.66
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000091237

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:04.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               7.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15958041.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.91
p-value of test                       :  9.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    3.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.15
p-value of test                       :    0.9986

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7227.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.03
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:51.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46311
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870311
  j =  1                              :        399907384
  j =  2                              :            46299
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908408
  j =  2                              :            45793
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.25e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.24
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.04
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.94
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.85
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.48
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  293.65
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.96
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.42
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.45
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.94
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000080284

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.03
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999946061

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.22
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:40.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16744473.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1236
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334356
  j =  1                              :        599997528
  j =  2                              :             1236
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6795.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.93
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908478
  j =  2                              :            45761
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908119
  j =  2                              :            45939
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.1e-3


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17737.81
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.29
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.07
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.43
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.80
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.36
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.24
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.62e-4
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.49
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000079663

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.00
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000011176

Normal statistic for number of bits   :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:08.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17793049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908229
  j =  2                              :            45878
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908665
  j =  2                              :            45666
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.10
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17730.80
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.63
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  608.18
p-value of test                       :  6.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.64
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.72
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.60
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.00
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.40
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.55
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:29.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5143.89
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.30
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999923408

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.70
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999947435

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:42.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    6.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18776089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9977

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    4.42
p-value of test                       :  5.5e-3

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.20
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.91
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.80
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908175
  j =  2                              :            45911
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907891
  j =  2                              :            46050
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    4.37
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17730.59
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.22
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.97
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.29
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.13
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.22
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  313.15
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.34
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.43
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.46
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999927209

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.41
p-value of test                       :  5.1e-3


-----------------------------------------------
Total number of bits:  7999947510

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:00.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19824665.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.73
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907825
  j =  2                              :            46080
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45419
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869419
  j =  1                              :        399909164
  j =  2                              :            45415
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.68
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.03
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.91
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.79
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.47
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.69
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.17
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000072373

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.72
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999977387

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:24.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 589842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9974

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.95
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.50
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908476
  j =  2                              :            45762
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908777
  j =  2                              :            45604
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.09
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.68
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  124.88
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.22
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.56
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.04
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.49
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.73
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12077.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999922595

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.49
p-value of test                       :    0.9910


-----------------------------------------------
Total number of bits:  7999994532

Normal statistic for number of bits   :  -0.043
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:43.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    2.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1277967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5574
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.02
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.93
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.38
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907666
  j =  2                              :            46167
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908194
  j =  2                              :            45894
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.82
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.00
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.93
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.21
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.54
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.21
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.23
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.65
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000108148

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.77
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000091603

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:57.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2588687.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.81
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.14
p-value of test                       :  7.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.41
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.46
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907623
  j =  2                              :            46181
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908373
  j =  2                              :            45812
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.12e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.15
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17614.57
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.90
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.86
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.04
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.72
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.37
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.35
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.03
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.36
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.29
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999894404

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.96
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999966773

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:26.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3801103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.70
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  283.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.31
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.90
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908050
  j =  2                              :            45966
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908585
  j =  2                              :            45703
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 9.62e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17178.28
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.22
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.50
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.55
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.16
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.61
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.30
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.33
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11564.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12101.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.33
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000059254

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.93
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000098812

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.47
p-value of test                       :    0.9932

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:39.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4816911.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    4.76
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.03
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7277.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.24
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908572
  j =  2                              :            45711
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908274
  j =  2                              :            45860
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.58
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.82
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.68
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.08
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.95
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.28
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4297.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.46
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000094042

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.59
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999917669

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:57.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5767183.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.91
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.49
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.47
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45603
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869603
  j =  1                              :        399908797
  j =  2                              :            45597
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.43e-4
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.02
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.01
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.80
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.08
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.21
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.97
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.52
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.41
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.85
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.85
p-value of test                       :  7.6e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.07
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12114.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11532.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.73
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000030688

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.52
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999910337

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:43.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6619151.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  184.99
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.98
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908080
  j =  2                              :            45954
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908175
  j =  2                              :            45911
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.30
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.01
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.02
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.48
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.33
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.69
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.53
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.27
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.58
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.76
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12090.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.53
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999971336

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999974630

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:18.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7700495.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.14
p-value of test                       :  7.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4882.86
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908017
  j =  2                              :            45987
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46339
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870339
  j =  1                              :        399907326
  j =  2                              :            46331
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.95e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 4.74e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17707.40
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.87
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.91
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.05
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.92
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.60
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  304.01
p-value of test                       :    0.9990    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.79e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.24
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.70
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.35
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000008554

Normal statistic for number of bits   :   0.068
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.77
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999965741

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:21.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8781839.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997255
  j =  2                              :             1371
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5257
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.41
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.39
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.82
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5182.03
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908690
  j =  2                              :            45649
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17814.37
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.67
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.07
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.89
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.32
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.52
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.06
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.65
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.18
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.26
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.58
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.47
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000151567

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.94
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999941120

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:42.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9732111.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9961

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1365.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.41
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.66
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.57
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908941
  j =  2                              :            45522
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908152
  j =  2                              :            45918
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.99
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.14
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17753.38
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.16
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.53
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.12
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.39
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.14
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11537.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.74
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000156664

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.98
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999988499

Normal statistic for number of bits   :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:05.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10649615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.41
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.82
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907890
  j =  2                              :            46049
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908690
  j =  2                              :            45649
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 6.90e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17190.22
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.87
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   37.83
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  491.27
p-value of test                       :  1.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.51
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.92
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.89
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.97
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.66
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999966953

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.94
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999777449

Normal statistic for number of bits   :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:42.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     0.9998 
 78  RandomWalk1 M (L=10000, r=0)    1.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11567119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.42
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:50.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46164
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870164
  j =  1                              :        399907675
  j =  2                              :            46158
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908141
  j =  2                              :            45922
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.43
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.74
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.59
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.42
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.33
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.39
p-value of test                       :  9.0e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.72
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.06
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999988325

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.90
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999855176

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:00.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12648463.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.81
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.52
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908269
  j =  2                              :            45861
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908720
  j =  2                              :            45628
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.54e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.47
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.79
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.60
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.25
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.85
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.84
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.75
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -401.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.18e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9935

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.89
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9750.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.89
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.37
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000044677

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.50
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000108886

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:07.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13729807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:33.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.96
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.22
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5326.58
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908794
  j =  2                              :            45600
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.16e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.89
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.87
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.16
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.90
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.21
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.62
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.68
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.13
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12111.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.55
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999959414

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000067990

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.048
p-value of test                       :    0.48

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:07.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14614529.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.68
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:53.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45431
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869431
  j =  1                              :        399909142
  j =  2                              :            45423
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908031
  j =  2                              :            45977
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.77
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   62.42
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.53
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.07
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.49
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.22
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.03
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:29.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4704.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12220.03
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.74
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999994196

Normal statistic for number of bits   :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.63
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000040237

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:25.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15630337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    3.26
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.01
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.60
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.27
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.83
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908418
  j =  2                              :            45782
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908643
  j =  2                              :            45674
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.52e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17571.68
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.63
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.16
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.07
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.91
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9758.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4673.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.61
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000084808

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.75
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000027487

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16646145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7060
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    3.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6878.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.09
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.33
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908382
  j =  2                              :            45806
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :  1.0e-2


-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.95
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.30
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.43
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.20
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.91
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.29
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.88
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.27
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9684.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3946.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.23
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999865631

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.21
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000025243

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:48.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17661953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    7.92
p-value of test                       :  1.4e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.14
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :  104.54
p-value of test                       :  4.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1542.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.62
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.83
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908377
  j =  2                              :            45804
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.95e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.039
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.19
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.95
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.98
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.39
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.76
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.78
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.40
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.33
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.49
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999932996

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.07
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999917654

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:41.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            1.4e-4
 33  CouponCollector, r = 27         4.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18644993.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9973

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  376.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.50
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.73
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907677
  j =  2                              :            46157
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907780
  j =  2                              :            46104
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.17e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.15
p-value of test                       :  8.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.95
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.19
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.06
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.19
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.22
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.25
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.89
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.54
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.07
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.02
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.96
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.78
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.56
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999947012

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.97
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999954551

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:06.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               8.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19595265.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.48
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907974
  j =  2                              :            46010
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908082
  j =  2                              :            45947
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17874.56
p-value of test                       :  9.0e-3



-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.81
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.17
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.55
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.63
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.79
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.30
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999993746

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.61
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999934166

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:07.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 622611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9918

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.08
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7274.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.58
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.00
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908492
  j =  2                              :            45748
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  4.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    5.10
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16891.25
p-value of test                       :    0.9982



-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.26
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.17
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.41
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.65
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.23e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4724.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.41
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999953306

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.04
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999923618

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:58.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1114131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.45
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:49.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908061
  j =  2                              :            45968
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908499
  j =  2                              :            45740
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.14
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17159.23
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.56
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.00
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.15
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.69
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.62
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.97
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5238.08
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.64
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.72
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.30
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.15
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999954749

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999987122

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         : 9.96e-3
p-value of test                       :    0.50

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:58.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2195475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.28
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4827.53
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907877
  j =  2                              :            46060
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907935
  j =  2                              :            46028
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.62
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17202.11
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.59
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.84
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.13
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.37
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.39
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.50
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.11
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999839345

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.73
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000085039

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    2.76
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:30.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3080211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    3.53
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9978

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.85
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.05
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46236
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870236
  j =  1                              :        399907528
  j =  2                              :            46236
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.97
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.98
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.48
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.67
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.71
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.07
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.75
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.60
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.00
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.03
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.71
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:32.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4686.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.3e-4    *****

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5117.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.12
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000098917

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.62
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999991319

Normal statistic for number of bits   :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:54:07.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4358174.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.28
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9983

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.90
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907779
  j =  2                              :            46106
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908047
  j =  2                              :            45972
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.53
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.47
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  402.40
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.97
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.16
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.40
p-value of test                       :  4.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.81
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9907

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.62
p-value of test                       :    0.9905

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9794.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.85
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000165409

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000017692

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 J (L=1000, r=0)     0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6029342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    4.23
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:47.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.51
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908700
  j =  2                              :            45650
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907870
  j =  2                              :            46059
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.16e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17344.06
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.69
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.74
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.51
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.12
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.74
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.80
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.86
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000213580

Normal statistic for number of bits   :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.95
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999959282

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:51.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7077918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:51.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.41
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.03
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908289
  j =  2                              :            45851
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908551
  j =  2                              :            45723
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.97
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.62
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.98
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.31
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.32
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.17
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000061201

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.34
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999940247

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:54.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8093726.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.64
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    7.28
p-value of test                       :  2.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:28.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.60
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.44
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908303
  j =  2                              :            45844
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908120
  j =  2                              :            45937
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.88
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.51
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.50
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.00
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.23
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.09
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.65
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.59e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.70
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000023404

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.80
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000032953

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:51.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         2.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9109534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.86
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6851.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.46
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5223.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908152
  j =  2                              :            45918
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45541
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869541
  j =  1                              :        399908920
  j =  2                              :            45537
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.53
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.83
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.97
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.77
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.26
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.73
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10352.86
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4597.00
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.61
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.69
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999958349

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.19
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999955484

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:58.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10125342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9959

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    4.26
p-value of test                       :  6.5e-3

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.46
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908111
  j =  2                              :            45937
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908501
  j =  2                              :            45742
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.54
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17141.87
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.27
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.81
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.84
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.84
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.81
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.68
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.43
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.46
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.62
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.71
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999923189

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.72
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000168976

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:43.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11141150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.23
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.03
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7249.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.09
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.71
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908339
  j =  2                              :            45829
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908576
  j =  2                              :            45712
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.85
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.13
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.50
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.76
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.45
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.46
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.56
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.42
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10336.00
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4696.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.25
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999995429

Normal statistic for number of bits   :  -0.036
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.49
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999991574

Normal statistic for number of bits   :  -0.067
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:51.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12124190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.88
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908522
  j =  2                              :            45733
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.36
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.92
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.66
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.80
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.49
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.03
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.46
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000063643

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.42
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999986132

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.79
p-value of test                       :  2.6e-3

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:12.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13139998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.92
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908623
  j =  2                              :            45684
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46308
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870308
  j =  1                              :        399907390
  j =  2                              :            46296
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.27
p-value of test                       :  5.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17093.05
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.71
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.55
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.52
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.21
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.73
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.13
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.07
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.18
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999998570

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.85
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000198190

Normal statistic for number of bits   :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:52.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               5.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14155806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.53
p-value of test                       :  4.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.85
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6798.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907980
  j =  2                              :            46001
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.17e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.01
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.45
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.93
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.01
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5186.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.92
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.16
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.50
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999989699

Normal statistic for number of bits   :  -0.081
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.94
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999844319

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:32.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15171614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:44.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.35
p-value of test                       :  6.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.02
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908486
  j =  2                              :            45748
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908288
  j =  2                              :            45853
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.38
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.58
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.43
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.91
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  272.36
p-value of test                       :  5.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.32
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.78
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.09
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.05
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.61
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.66
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.66
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:29.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.48
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000132739

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.22
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999976571

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:34.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    5.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16121886.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.34
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.99
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.96
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908396
  j =  2                              :            45793
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908146
  j =  2                              :            45924
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.77
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.59
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.85
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.73
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.34
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5098.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.18
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000023926

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.53
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000033202

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:14.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17170462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9969


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.14
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.79
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.10
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907795
  j =  2                              :            46098
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908775
  j =  2                              :            45602
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.75
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.51
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.82
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.26
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.15
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.09
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.13
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  149.80
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:34.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.40
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000066358

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.11
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000179977

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:55.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18153502.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9946

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.66
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.06
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908062
  j =  2                              :            45957
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908450
  j =  2                              :            45763
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.32
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.33
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.76
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.69
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.80
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.26
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.51
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.88
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:29.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5134.06
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3860.75
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.45
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000155278

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   89.70
p-value of test                       :  1.6e-3


-----------------------------------------------
Total number of bits:  7999911180

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19169310.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1541.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:20.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.88
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908183
  j =  2                              :            45907
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908355
  j =  2                              :            45818
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.58e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.26
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.05
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.03
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.66
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.69
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4822.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.33
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.67
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.89
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.09
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.49
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.12
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5096.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.31
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000077989

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.90
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999984776

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    2.76
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:38.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20086814.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  511.92
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.21
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.50
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.47
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:56.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908515
  j =  2                              :            45738
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908076
  j =  2                              :            45953
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.34
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.42
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.90
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.17
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.97
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.99
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.58
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.50
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.55
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.19
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.09
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.38
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.12
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.57
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.45
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999897494

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.65
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999805307

Normal statistic for number of bits   :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:19.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 655380.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9932

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7273.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.24
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.86
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:52.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908429
  j =  2                              :            45781
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907751
  j =  2                              :            46120
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    5.40
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:28.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.52
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.24
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.79
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.00
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.86
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.91
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.57
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.57
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.60
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.40
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.27
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:31.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.47
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000086449

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.68
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999961358

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:34.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1769473.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6680.57
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.44
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4801.76
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908016
  j =  2                              :            45989
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908374
  j =  2                              :            45804
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    4.37
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  3.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
p-value of test                       : 1 -  6.1e-5    *****

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:29.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.88
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.13
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.91
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.88
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.36
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.51
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.90
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.58
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.50
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.53
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.07
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:35.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12205.73
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.78
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999969368

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.98
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000006886

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:50.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 37  Gap, r = 20                     0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2424833.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7538
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6864.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.60
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.50
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.17
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908519
  j =  2                              :            45739
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908539
  j =  2                              :            45720
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.13
p-value of test                       :  8.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:29.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.47
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.31
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.57
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.54
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.61
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.62
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.54
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.34
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.06
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.50
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000027553

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000044266

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    2.46
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:32.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               8.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3211265.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9982

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.14
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907990
  j =  2                              :            46002
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908498
  j =  2                              :            45748
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.36
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.80
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.08
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.07
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.86
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.46
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.22
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10358.10
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.41
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000075448

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.40
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999841757

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:33.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4620289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9960

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  279.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  372.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.88
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.32
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907675
  j =  2                              :            46161
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46327
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870327
  j =  1                              :        399907349
  j =  2                              :            46321
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.07
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.49
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.92
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.61
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.86
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.12
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.68
p-value of test                       :    0.9996    *****

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4332.84
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.30
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999920936

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.45
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000022372

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:22.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5865473.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7564
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.07
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4909.49
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908283
  j =  2                              :            45851
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908362
  j =  2                              :            45816
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:10.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9952


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    5.43
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.22
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.75
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.62
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   93.63
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.56
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.55
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.75
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.33
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5184.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.43
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.42
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.10
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   44.00
p-value of test                       :  2.8e-4    *****



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4681.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.72
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999981500

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.84
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000019537

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:23.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6881281.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.04
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6828.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5202.08
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907992
  j =  2                              :            46001
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46113
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870113
  j =  1                              :        399907778
  j =  2                              :            46105
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.21
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.80
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.39
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.35
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.60
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.03
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.20
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.22
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.60e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.03
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.49
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.81
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000144223

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.46
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999835898

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.23
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:55.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7929857.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9926

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    3.03
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.91
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:50.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6805.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.48
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907942
  j =  2                              :            46026
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46353
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870353
  j =  1                              :        399907300
  j =  2                              :            46341
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.61
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.78
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.06
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.64
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.07
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.58
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.78
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000076093

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.54
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000021673

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9942

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:09.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8945665.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4170
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.54
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907603
  j =  2                              :            46194
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907930
  j =  2                              :            46032
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.99e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 8.06e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.94
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.10
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.64
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.16
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.59
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.34
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.39
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.03e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.22
p-value of test                       :    0.9964

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10220.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.85
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999966737

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.14
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000005854

Normal statistic for number of bits   :   0.046
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:53.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9895937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1494
p-value of test                       :  2.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334614
  j =  1                              :        599997012
  j =  2                              :             1494
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5565
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.44
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.07
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.30
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:29.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.22
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.86
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46302
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870302
  j =  1                              :        399907398
  j =  2                              :            46298
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 3.55e-4
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17045.15
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.78
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.03
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.57
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.44
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.49
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.12
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.22
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.21
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   41.43
p-value of test                       :  4.2e-5    *****


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.54
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.71
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.38
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000091159

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.18
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000076639

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           2.8e-4
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               4.2e-5
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10911745.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5294
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.11
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.65
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908465
  j =  2                              :            45766
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908277
  j =  2                              :            45851
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-6
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17014.32
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.39
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  587.19
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.40
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.86
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.26
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  145.73
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.000
p-value of test                       :    0.50

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    2.81
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.53
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:30.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.02
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000085150

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.22
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000063652

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:46.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11862017.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9948


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.65
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6835.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.16
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908264
  j =  2                              :            45859
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908296
  j =  2                              :            45849
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.58e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.93
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.19
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.30
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.14
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.55
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.91
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.37
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.16
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.22
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.40
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999928775

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.43
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000017215

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:26.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12812289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.97
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.52
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.76
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907908
  j =  2                              :            46040
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908243
  j =  2                              :            45871
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.48
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.10
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4824.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.56
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.10
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:29.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.97
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999952916

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.92
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000018103

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:36.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13664257.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.57
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4913.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908711
  j =  2                              :            45640
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45406
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869406
  j =  1                              :        399909193
  j =  2                              :            45396
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.05
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  178.23
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.21
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.62
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.08
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.50
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.37
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.60
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.56
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.80
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.26
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.27
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.27
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.99
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000046783

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.87
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999973211

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:03.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14647311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.00
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.38
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     185
p-value of test                       :  3.2e-3

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.67
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.41
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907792
  j =  2                              :            46098
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908849
  j =  2                              :            45568
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.55e-4
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.32
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.69
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.44
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.25
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12125.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.73
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000024424

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.54
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000040594

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:23.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15695887.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     653
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   98.12
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.60
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.39
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907644
  j =  2                              :            46175
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907803
  j =  2                              :            46091
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.11
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.47
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.52
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.99
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.56
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.02
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.39
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.24
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.30
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.10
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.76
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.24
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.23
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9730.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -1.40e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:28.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.32
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000084562

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.65
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000069193

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:05.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17039375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    3.76
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.32
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.63
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908060
  j =  2                              :            45961
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908016
  j =  2                              :            45992
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.67e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16889.75
p-value of test                       :    0.9983



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.77
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.21
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.00
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.78
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.79
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    6.90
p-value of test                       :  4.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.47
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:28.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.35
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999971675

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.57
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999947795

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:47.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17924111.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9919

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    4.27
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    3.35
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.99
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.84
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.48
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:45.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45538
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869538
  j =  1                              :        399908931
  j =  2                              :            45524
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907945
  j =  2                              :            46023
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.69e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.35
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.39
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.03
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.32
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.12
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.86
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.68
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.69
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.77
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.50
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999973766

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.15
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999980468

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         : -8.92e-3
p-value of test                       :    0.50

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:15.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18841615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9937

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7265.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.59
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908521
  j =  2                              :            45735
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907994
  j =  2                              :            46000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.8e-3


-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.95
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.68
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.36
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.37
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.69
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.33
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.90
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.72
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999906311

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.63
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000151339

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:47.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19759119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     343
p-value of test                       :  8.0e-3

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.91
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.58
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4867.34
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908847
  j =  2                              :            45572
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.50
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.94
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.96
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.94
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.24
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.52
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999986711

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.30
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999851726

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 688149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.81
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7319.46
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.14
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.91
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:00.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907704
  j =  2                              :            46145
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908317
  j =  2                              :            45834
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.90e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17004.77
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.36
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   94.22
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.09
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.80
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.56
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.71
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.34
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.68
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.62e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.27
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.05
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999946055

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.83
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000112876

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:36.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 H (L=1000, r=20)    0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1343509.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.42
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    5.08
p-value of test                       :  2.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    5.12
p-value of test                       :  2.5e-3

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.31
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.82
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907961
  j =  2                              :            46018
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908508
  j =  2                              :            45737
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.25e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   67.18
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.36
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.65
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   50.61
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.99
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.23
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10270.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.38
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.96
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000025894

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.16
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000013786

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:23.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2949141.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5537
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4151
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9993    *****

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.38
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.05
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6909.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4885.32
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908652
  j =  2                              :            45674
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907959
  j =  2                              :            46016
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.87
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.02
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.92
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.35
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.24
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.99
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.15
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.20
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.95
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.42
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000051088

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000089035

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:41.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3932181.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.98
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:20.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.75
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:58.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908744
  j =  2                              :            45628
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908245
  j =  2                              :            45876
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.73
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.36
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.84
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.74
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.04
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.51
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.21
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.94
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.93
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.48
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.34
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.41
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.50
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:34.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.02
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000030328

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.45
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999971408

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:47.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4915221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    4.70
p-value of test                       :  4.0e-3

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.30
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.74
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.66
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399907998
  j =  2                              :            45998
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907800
  j =  2                              :            46091
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:09.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.03
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.49
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.39
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.67
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.89
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.26
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999922361

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.77
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999997406

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:35.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5898261.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    4.36
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.07
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.66
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908007
  j =  2                              :            45995
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908189
  j =  2                              :            45901
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.00
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.85
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.88
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.59
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.19
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.70
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.14
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.49
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.97
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.57
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000001789

Normal statistic for number of bits   :   0.014
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.96
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000076270

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6848533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:33.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9980


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.21
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.25
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.67
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907999
  j =  2                              :            45993
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908596
  j =  2                              :            45693
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :  3.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.08
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17871.14
p-value of test                       :  9.5e-3



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.65
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.98
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.56
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.12
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.73
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.16
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.01
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.73
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.27
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.86
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:33.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.44
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999805202

Normal statistic for number of bits   :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.42
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000058324

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:23.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7798804.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1236
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334356
  j =  1                              :        599997528
  j =  2                              :             1236
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4148
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.92
p-value of test                       :  9.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.81
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.58
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:47.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5155.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908551
  j =  2                              :            45717
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907614
  j =  2                              :            46184
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17150.39
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.89
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.24
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.87
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.35
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.98
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.72
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.25
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.00
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.20
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000116899

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.01
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000053062

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:17.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8912916.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    3.22
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7314.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4825.69
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908324
  j =  2                              :            45832
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908615
  j =  2                              :            45691
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  8.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-5
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    : 3.62e-4
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.48
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.47
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.19
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.65
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.99
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.55
p-value of test                       :  5.3e-3

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:31.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999967943

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.71
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999998162

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:00.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10092564.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:46.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:48.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.72
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.63
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.58
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907740
  j =  2                              :            46127
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907771
  j =  2                              :            46113
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:15.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 8.96e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.82
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.020
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.86
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.20
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.87
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.09
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.79
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  292.37
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.33
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.20
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999976610

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000078190

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.67
p-value of test                       :  2.6e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    6.56
p-value of test                       :  5.8e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.21
p-value of test                       :    0.9993    *****

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.030
p-value of test                       :    0.51

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:22.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        0.9992 
 79  RandomWalk1 R (L=10000, r=15)   0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 103  AutoCor, d=1, r=0               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11108372.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    3.91
p-value of test                       :  9.6e-3

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   95.49
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:28.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908635
  j =  2                              :            45678
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908116
  j =  2                              :            45933
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.99
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.17
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.74
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.31
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.61
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.25
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.13
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.15
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.48
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.18
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999911195

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.36
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000106117

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  1.0e-2

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:09.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12156948.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.22
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.96
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907647
  j =  2                              :            46172
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908248
  j =  2                              :            45870
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-5
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    5.37
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16857.84
p-value of test                       :    0.9990    *****



-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.46
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.93
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.38
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.35
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.06
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:59.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9804.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4317.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.92
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999961964

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999924875

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:49.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 73  GCD                             0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13172756.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.73
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.54
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.73
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.69
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908620
  j =  2                              :            45684
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.48
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.54
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.53
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.70
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.18
p-value of test                       :  4.6e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.79
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999923276

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.51
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000005857

Normal statistic for number of bits   :   0.046
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    2.96
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:10.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14090260.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.17
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.59
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908085
  j =  2                              :            45953
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908093
  j =  2                              :            45949
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  9.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.62e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.76e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17159.13
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.22
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.72
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.40
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.20
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.65
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.81
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:30.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   92.15
p-value of test                       :  9.4e-4    *****


-----------------------------------------------
Total number of bits:  7999982661

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.54
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999903095

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 101  Run of bits, r = 0              9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15138836.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5289
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9919


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.16
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.38
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907750
  j =  2                              :            46122
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907771
  j =  2                              :            46104
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.05
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.28
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.89
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.74
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.32
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.21
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.64
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.64
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -403.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.02

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.25
p-value of test                       :    0.9962

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -3.19e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11498.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.13
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999998654

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.83
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999953360

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         : -5.80e-4
p-value of test                       :    0.50

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:41.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16187412.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.85
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.86
p-value of test                       :  3.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.64
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:29.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.38
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907774
  j =  2                              :            46107
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907673
  j =  2                              :            46156
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.32
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.47
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.75
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.60
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.64
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.48
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.94
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.95
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.30
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.71
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000006751

Normal statistic for number of bits   :   0.053
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.58
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000024850

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.20
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:46.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17235988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    4.65
p-value of test                       :  4.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     190
p-value of test                       :  9.3e-4    *****

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:29.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.98
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46342
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870342
  j =  1                              :        399907318
  j =  2                              :            46338
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907688
  j =  2                              :            46153
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17695.31
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.95
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.98
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.34
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.44
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.49
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.16
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.22
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.82
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000168832

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.53
p-value of test                       :    0.9938


-----------------------------------------------
Total number of bits:  8000096775

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       9.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18251796.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.11
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    5.18
p-value of test                       :  2.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     119
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.46
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5208.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907840
  j =  2                              :            46077
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907926
  j =  2                              :            46031
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.03
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.04
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.80
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.73
p-value of test                       :    0.9995    *****

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 6.15e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.43
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000003358

Normal statistic for number of bits   :   0.027
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.55
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000069784

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:34.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19267604.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    3.35
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.06
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908341
  j =  2                              :            45828
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45498
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869498
  j =  1                              :        399909005
  j =  2                              :            45496
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  5.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17665.90
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.60
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.38
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.05
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.29
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.58
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.43
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3946.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.26
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000112582

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.78
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000029851

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.89
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:36.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20250644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.35
p-value of test                       :  2.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.92
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  162.61
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.97
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908345
  j =  2                              :            45823
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -3.37e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17647.22
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.14
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.87
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.18
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.63
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.47
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.06
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.64
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11524.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000024094

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.27
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000170434

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:07.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 720918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.73
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6788.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.75
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5169.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908603
  j =  2                              :            45691
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908810
  j =  2                              :            45586
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-4
p-value of test                       :    0.9990

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.55
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.59
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.79
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.06
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.91
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.36
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5170.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.19
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.50
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.92
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999999956

Normal statistic for number of bits   : -3.48e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.65
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000091213

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:46.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1146902.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9919

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:31.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.40
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4862.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908794
  j =  2                              :            45600
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908110
  j =  2                              :            45942
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    : 4.30e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.66
p-value of test                       :  4.1e-5    *****

Anderson-Darling statistic = A2       :    6.55
p-value of test                       :  5.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.46
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17058.13
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.82
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.69
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.09
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.07
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.77
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.04
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 3.46e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11518.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.48
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999933509

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.28
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000024610

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:16.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2064406.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     186
p-value of test                       :  2.5e-3

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.07
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:52.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908604
  j =  2                              :            45689
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908257
  j =  2                              :            45867
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.85
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.53
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.23
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.51
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.19
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.88
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.18
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.82
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.16
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10250.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.36
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000000247

Normal statistic for number of bits   : 1.95e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.21
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000070729

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3112969.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.14
p-value of test                       :    0.9989


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.02
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.13
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908252
  j =  2                              :            45868
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.47
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.85
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.88
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.52
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.64
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.12
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.78
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.37
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-4
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.31
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.56
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999932627

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.27
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999990467

Normal statistic for number of bits   :  -0.075
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:05.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4063241.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    3.84
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  352.13
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.57
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908895
  j =  2                              :            45545
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908309
  j =  2                              :            45841
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:19.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.16
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.59
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.69
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.43
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.90
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.29
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.74
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.95
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.13e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.01
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.70
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999803303

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.68
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000120109

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:02.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5079049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908578
  j =  2                              :            45699
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908507
  j =  2                              :            45742
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.97
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   39.73
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.93
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.35
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.97
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.77
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.56
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.96
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.43
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9602.84
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.83
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999916973

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.65
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000016165

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.061
p-value of test                       :    0.48

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6094857.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.72
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.54
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908047
  j =  2                              :            45975
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907894
  j =  2                              :            46050
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.70
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.67
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.22
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.36
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.32
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.96
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.71
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.09
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.14
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.89
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000068248

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.42
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000095467

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:44.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7110665.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.59
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.18
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908133
  j =  2                              :            45932
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908329
  j =  2                              :            45831
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.06
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.47
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.30
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.17
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.76
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.84
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.51
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.95
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.77
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.4e-4    *****

Anderson-Darling statistic = A2       :    6.55
p-value of test                       :  5.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5218.77
p-value of test                       :  5.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.91
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4588.36
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.59
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000088249

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.39
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999881900

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.083
p-value of test                       :    0.53

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:00.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 95  HammingIndep, L=30, r=0         5.6e-4
 96  HammingIndep, L=30, r=27        0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8192009.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    4.88
p-value of test                       :  3.3e-3

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.09
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5332.38
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908370
  j =  2                              :            45812
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908764
  j =  2                              :            45615
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:19.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 6.49e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17373.11
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.85
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.03
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4670.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.73
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.80
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999989801

Normal statistic for number of bits   :  -0.081
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.57
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000064171

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    2.43
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:23.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9207817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.68
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.71
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46258
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870258
  j =  1                              :        399907487
  j =  2                              :            46252
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908701
  j =  2                              :            45645
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.68
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   41.36
p-value of test                       :  8.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.20
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.30
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.47
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.67
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.93
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.95
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10286.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:25.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.19
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000019210

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999936752

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:30.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 C (L=50, r=0)       8.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10223625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.40
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.51
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4916.84
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908524
  j =  2                              :            45738
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907645
  j =  2                              :            46173
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17789.08
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.43
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.10
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.65
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.08
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.04
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -401.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.50
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.58
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.65
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:29.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5137.10
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.04
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000025834

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.76
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999955370

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:06.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11239433.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4810.73
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46264
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870264
  j =  1                              :        399907475
  j =  2                              :            46258
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908006
  j =  2                              :            45994
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.95
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:29.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:29.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.74
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.88
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.97
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.62
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.77
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.76
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.26
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.64
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.04
p-value of test                       :  4.8e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.13
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.33
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999996863

Normal statistic for number of bits   :  -0.025
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.46
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999959216

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:53.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12255241.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5271
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9945

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.79
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.52
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908018
  j =  2                              :            45985
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908533
  j =  2                              :            45729
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:19.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   67.50
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17819.92
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.75
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.19
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.25
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.85
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -401.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10295.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3938.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.45
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999961064

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000153229

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:03.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13303817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.80
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.56
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908539
  j =  2                              :            45726
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908819
  j =  2                              :            45589
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:29.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:29.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.17
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.27
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.96
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.37
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.96
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   90.42
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.75
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.30
p-value of test                       :    0.9931


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.26
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10262.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999886178

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.97
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999965678

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:14.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14319625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.69
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.14
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.43
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908182
  j =  2                              :            45903
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907994
  j =  2                              :            46000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17774.72
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.25
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.67
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.83
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.76
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-5
p-value of test                       : 1 -  7.6e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    5.19
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5249.65
p-value of test                       :  1.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3943.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.52
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999969527

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.87
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000059365

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 96  HammingIndep, L=30, r=27        1.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15302665.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.42
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907984
  j =  2                              :            46002
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:29.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:29.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.093
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.55
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.50
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.28
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.96
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.94
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.26
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.59
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.40
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.18
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.52
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    1.73
p-value of test                       :    0.9997    *****


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11453.17
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.60
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999941516

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.05
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999937820

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:23.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               0.9997 
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16416777.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.39
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907995
  j =  2                              :            45995
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908549
  j =  2                              :            45718
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.66
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17011.91
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.94
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.18
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.13
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.38
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.39
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.14
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.61
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.91
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.99e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9682.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.49
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000153601

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.49
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000011272

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:36.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17432585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7090
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7267.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.11
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.70
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45384
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869384
  j =  1                              :        399909234
  j =  2                              :            45380
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.72
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.77
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.03
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.14
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.39
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  453.72
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.77
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.69
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:44.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.87
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000141688

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.66
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999997370

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:31.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18448393.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.59
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7281.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.86
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.33
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908494
  j =  2                              :            45750
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908438
  j =  2                              :            45778
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.69
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.82
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.70
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.93
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5196.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.63
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  141.33
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.00
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.25
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.34e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.73
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000036178

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.82
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000013132

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:19.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                0.9994 
 79  RandomWalk1 C (L=10000, r=15)   0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19464201.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.67e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:28.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908131
  j =  2                              :            45933
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907931
  j =  2                              :            46027
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.01
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.09
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.43
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.04
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.75
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.58
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.03
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.58
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.24
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:35.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5112.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.46
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999946784

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.21
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999777635

Normal statistic for number of bits   :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:52.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 753687.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.07
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.87
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908160
  j =  2                              :            45917
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46278
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870278
  j =  1                              :        399907445
  j =  2                              :            46276
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:15.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.30
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.52
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.40
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.89
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.11
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.57
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   25.69
p-value of test                       :  1.2e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3912.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.62
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000023848

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.36
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000091615

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:57.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1966103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5537
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9944


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9971


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  302.63
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.09
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:28.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.93
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5223.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908641
  j =  2                              :            45675
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908455
  j =  2                              :            45771
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.33
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.66
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.07
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.66
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.95
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.74
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.31
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000053800

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.60
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000031996

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:46.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2981911.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:48.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:28.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.97
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.64
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45354
p-value of test                       :    0.9930


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869354
  j =  1                              :        399909293
  j =  2                              :            45352
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908412
  j =  2                              :            45788
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.84
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.49
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.06
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.99
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  589.67
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5324.90
p-value of test                       :  7.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.55
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.40
p-value of test                       :  4.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11405.03
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.54
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.64
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999967643

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.26
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999923702

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.010
p-value of test                       :    0.50

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:51.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    7.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4030487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     840
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9947

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:28.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.88
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:55.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907882
  j =  2                              :            46056
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.98
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.79
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.10
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.82
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.07
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.50
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10359.48
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9957

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.59
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000093568

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.81
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000031672

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.84

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:12.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4980759.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4521
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.66
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.78
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.26
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4915.04
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907993
  j =  2                              :            46002
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908451
  j =  2                              :            45770
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.82
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.33
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.15
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.87
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.55
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.09
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.29
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.94
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.40
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10268.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.22
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.67
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000116965

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.50
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999866669

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6062103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.56
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.69
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908152
  j =  2                              :            45918
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907979
  j =  2                              :            46006
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   21.47
p-value of test                       :  8.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.31
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.71
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.91
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.15
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.16
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.84
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.82
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.80
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.16
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.10
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.29
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10223.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -8.25e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12107.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.26
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999947879

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.14
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999938336

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:17.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        8.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7045143.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:48.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.28
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.20
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908108
  j =  2                              :            45946
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908378
  j =  2                              :            45808
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.56
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.27
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.71
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.51
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.52
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.50
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.95
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.24
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000005923

Normal statistic for number of bits   :   0.047
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.94
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999962621

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:10.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8060951.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6816.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.21
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908212
  j =  2                              :            45888
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908700
  j =  2                              :            45647
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:14.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.01
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.00
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.63
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.99
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.04
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.42
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.26
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.29
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.84
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.47
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.97
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.22
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999794714

Normal statistic for number of bits   :   -1.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.36
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999999023

Normal statistic for number of bits   : -7.72e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:56.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9043991.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    5.66
p-value of test                       :  1.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     533
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:16.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:48.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6825.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:28.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5284.65
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:54.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908669
  j =  2                              :            45661
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908022
  j =  2                              :            45983
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.44e-4
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.46
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.84
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.48
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.48
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.68
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.52
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.37
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9706.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:32.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.57
p-value of test                       :    0.9958


-----------------------------------------------
Total number of bits:  8000004042

Normal statistic for number of bits   :   0.032
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.15
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000032746

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.84

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9994263.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.52
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5224.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907978
  j =  2                              :            46005
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907904
  j =  2                              :            46045
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.35
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.26
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.52
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.29
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.41
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.46
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -6.91e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.60
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999854252

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.02
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999888053

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:19.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11010071.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.44
p-value of test                       :  5.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.73
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908284
  j =  2                              :            45858
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908051
  j =  2                              :            45970
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.08
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.51
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.41
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.10
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.71
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.20
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999871595

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.00
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999985622

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:56.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12091415.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6786.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:28.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.65
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:48.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908134
  j =  2                              :            45927
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908382
  j =  2                              :            45806
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.65e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.25e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-5
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.77
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.34
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.20
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.62
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.09
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.19
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3918.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.65
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999962894

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.54
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000102763

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13074455.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.13
p-value of test                       :  7.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.88
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.99
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908026
  j =  2                              :            45984
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908326
  j =  2                              :            45834
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.64
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.69
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.72
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.31
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.72
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.69
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.40
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.23
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.72
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.00
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000078700

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.38
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000080371

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.12
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:14.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14188567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9970

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:47.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.28
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.17
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:29.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.34
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:47.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45430
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869430
  j =  1                              :        399909141
  j =  2                              :            45428
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907912
  j =  2                              :            46038
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.75
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.25
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.48
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.91
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.62
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.93
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.55
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.00
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.58
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.17
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.36
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.81
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999945458

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.26
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000020221

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15204375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    4.26
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9981

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:47.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.16
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.05
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.20
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908142
  j =  2                              :            45926
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908337
  j =  2                              :            45827
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.2e-4    *****

Anderson-Darling statistic = A2       :    4.80
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    4.96
p-value of test                       :  3.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17147.42
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.77
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.18
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -401.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:29.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.84
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000199351

Normal statistic for number of bits   :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.69
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000003427

Normal statistic for number of bits   :   0.027
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:07.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16154647.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:47.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.91
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1297.64
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.16
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:47.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908358
  j =  2                              :            45818
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907835
  j =  2                              :            46078
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.99
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.99
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.78
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.13
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.98
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.72
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.00
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:29.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5132.86
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.67
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999990908

Normal statistic for number of bits   :  -0.072
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.28
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999993170

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17137687.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7534
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7607
p-value of test                       :  4.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9956


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  178.29
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.70
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908200
  j =  2                              :            45897
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908474
  j =  2                              :            45760
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.62e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.63
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.72
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.48
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.54
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.44
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.12
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.61
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.63
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.94
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.57
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4685.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.45
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000097090

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000090607

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.40
p-value of test                       :  8.1e-3

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:53.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        4.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18120727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.65
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.20
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908400
  j =  2                              :            45794
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908558
  j =  2                              :            45715
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17763.99
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.38
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5218.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.42
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.32
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.19
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.24
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.07e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.70
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.35
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999923225

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.53
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999905180

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:21.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2S, t = 5         0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19070999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.56
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6820.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.08
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908525
  j =  2                              :            45736
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907958
  j =  2                              :            46021
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9975


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.79
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.90
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.97
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.98
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.21
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.69
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.29
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.12
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.05
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9697.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:24.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.12
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.01
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999925196

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.61
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000027196

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:10.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20185111.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.24
p-value of test                       :  6.8e-3

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    4.85
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6811.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.13
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.23
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907940
  j =  2                              :            46024
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.99
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.61
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.96
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.24
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.08
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.29
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.33
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.36
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999931121

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.76
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999963392

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:28.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 786456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    6.10
p-value of test                       :  8.9e-4    *****

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.52
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  499.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.54
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.25
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908302
  j =  2                              :            45843
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908757
  j =  2                              :            45617
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.36e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.85
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.39
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.37
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.76
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5221.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.08
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.81
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.11
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.19
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   32.93
p-value of test                       :  9.9e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -403.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :-2.11e-16
p-value of test                       :    0.50

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999946631

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.85
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000087196

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.49
p-value of test                       :    0.9936

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:45.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          8.9e-4
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               9.9e-4
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1835032.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5591
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     998
p-value of test                       :  6.9e-4    *****

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.32
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908541
  j =  2                              :            45728
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908224
  j =  2                              :            45882
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.27e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17139.90
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.78
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.52
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.34
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.66
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5328.94
p-value of test                       :  6.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.43
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.18
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.57
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.89
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.86e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.83
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.55
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999864881

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.54
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999950216

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.49
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:11.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        6.9e-4
 78  RandomWalk1 J (L=10000, r=0)    6.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2654232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4495
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    4.81
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4722.81
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908127
  j =  2                              :            45935
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908010
  j =  2                              :            45992
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.37
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   95.14
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.54
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  147.24
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.58
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.42
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.85
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.70
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11458.09
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12087.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.32
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999942716

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.30
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999963293

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:06.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              0.9993 
 77  RandomWalk1 H (L=1000, r=20)    0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3899416.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.55
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:46.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908331
  j =  2                              :            45827
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46302
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870302
  j =  1                              :        399907398
  j =  2                              :            46298
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.05
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.97
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.47
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.07
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.91
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.13
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.59
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.01
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.18
p-value of test                       :  7.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.99
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000023512

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.45
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000198106

Normal statistic for number of bits   :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.57
p-value of test                       :    0.9949

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.089
p-value of test                       :    0.54

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:29.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 92  HammingCorr, L = 30             7.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4849688.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5200
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.10e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:27.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.21
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.66
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:46.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46197
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870197
  j =  1                              :        399907613
  j =  2                              :            46183
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908332
  j =  2                              :            45831
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.27
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.24
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.39
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.96
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.57
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.48
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.66
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999816413

Normal statistic for number of bits   :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.55
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000095587

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:18.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5734424.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.52
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.19
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.58
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46478
p-value of test                       :  2.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870478
  j =  1                              :        399907044
  j =  2                              :            46478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908119
  j =  2                              :            45933
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.32
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.22
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.89
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.52
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.27
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.54
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.69
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.27
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999903599

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.77
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999991415

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:41.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6651924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.51
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.64
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908290
  j =  2                              :            45852
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907960
  j =  2                              :            46014
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-4
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17102.39
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.69
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.14
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.98
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.16
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.26
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000107149

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.52
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000046495

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    3.16
p-value of test                       :  7.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:26.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7831573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5581
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.84
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6877.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.17
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907873
  j =  2                              :            46056
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46444
p-value of test                       :  4.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870444
  j =  1                              :        399907115
  j =  2                              :            46438
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.59
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.016
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17345.19
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.74
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.55
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.62
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.79
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.61
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.89
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.86
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.29
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.77
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.69e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5124.10
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.78
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999910463

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000029392

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:00.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8814613.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1538.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.06
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.04
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908038
  j =  2                              :            45975
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908688
  j =  2                              :            45656
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.12
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.26
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.92
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.65
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.21
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.82
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.17
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000104530

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.08
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999779948

Normal statistic for number of bits   :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:47.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9764885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7080
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7263.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   99.02
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.13
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.98
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908063
  j =  2                              :            45964
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908534
  j =  2                              :            45733
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.06
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.95
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17041.63
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.22
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.56
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.36
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.49
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.09
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.65
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.49
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.87
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.88
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.13
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12079.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.54
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999944903

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.66
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000048667

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10682389.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.93
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.25
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.57
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:52.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908080
  j =  2                              :            45957
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908708
  j =  2                              :            45646
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.37e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.44
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.98
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.03
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.56
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.02
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  115.94
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.82
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.00
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.55
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12297.89
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.51
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999985382

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.68
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000127915

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:31.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11632661.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.54
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.03
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45482
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869482
  j =  1                              :        399909037
  j =  2                              :            45480
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908243
  j =  2                              :            45874
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.88
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.11
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17671.56
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.33
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.91
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.73
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.66
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.70
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.31
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.58
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999946859

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999958439

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:59.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12681237.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5576
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  183.96
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.95
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:51.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907895
  j =  2                              :            46045
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908711
  j =  2                              :            45640
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17120.00
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.63
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.81
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.61
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.89
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.46
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:29.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3894.45
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.66
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999989606

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.35
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999992075

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:28.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13795338.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997143
  j =  2                              :             1427
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7539
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.74
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.38
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908324
  j =  2                              :            45829
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907814
  j =  2                              :            46090
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.56
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.76
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.68
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.29
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.47
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.55
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.41
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4762.79
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.56
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.11
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.92
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.49
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.63
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.77
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.90
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.90
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999802952

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.46
p-value of test                       :    0.9911


-----------------------------------------------
Total number of bits:  8000026095

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14843914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9985

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.81
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4898.89
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908276
  j =  2                              :            45856
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907736
  j =  2                              :            46126
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.84e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17224.47
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.13
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.90
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.06
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.19
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.55
p-value of test                       :    0.9903


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 2.57e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:33.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.49
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.60
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000019198

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.66
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000089287

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         : -3.02e-3
p-value of test                       :    0.50

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:50.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15826954.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.70
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     660
p-value of test                       :  8.3e-3

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.16
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.89
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.61
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908054
  j =  2                              :            45964
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907931
  j =  2                              :            46027
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.55
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.07
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.12
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.03
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.22
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.95
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.14
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.26
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.49
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:03:28.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3927.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.52
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999999275

Normal statistic for number of bits   : -5.73e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.70
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000047608

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:00.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16875530.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.99
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9951

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.94
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4803.49
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907968
  j =  2                              :            46010
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908658
  j =  2                              :            45668
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.89
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9983


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.52
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.70
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.54
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.85
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.64
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.91
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.40
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.00
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000055132

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999971411

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   0.083
p-value of test                       :    0.47

Sample variance                       :    3.03
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:30.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17858570.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:37.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:26.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.48
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4862.89
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908532
  j =  2                              :            45728
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:15.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.39
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.87
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.21
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.22
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.62
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.33
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.76
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.97
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.67
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000148171

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.43
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999966152

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         : 7.54e-3
p-value of test                       :    0.50

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    2.79
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:23.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19005450.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9944

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:47.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.64
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.25
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908128
  j =  2                              :            45924
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908615
  j =  2                              :            45691
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17762.05
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.03
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.13
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.08
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.95
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999961628

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.92
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000003079

Normal statistic for number of bits   :   0.024
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:18.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19955722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.92
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.07
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907645
  j =  2                              :            46173
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908217
  j =  2                              :            45884
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.61
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17210.13
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.76
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.75
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.05
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.79
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.46
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.42
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.18
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.87
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.56
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.76
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000103219

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.03
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000089476

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:38.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 819225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4529
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.17
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.20
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907800
  j =  2                              :            46091
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908417
  j =  2                              :            45787
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.85
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.76
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.73
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.15
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.72
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.69
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.95
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.72
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999887174

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.13
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999972461

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.030
p-value of test                       :    0.51

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:29.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1900569.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45431
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869431
  j =  1                              :        399909142
  j =  2                              :            45423
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908093
  j =  2                              :            45949
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:14.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.96
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.61
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.60
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.91
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.27
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.61
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5217.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.98
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.82
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.37e-4
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.56
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10293.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11500.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.04
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999995465

Normal statistic for number of bits   :  -0.036
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.82
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999965696

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:57.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2818073.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4206
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9992    *****

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.14
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.82
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.51
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907660
  j =  2                              :            46167
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908277
  j =  2                              :            45854
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.83e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.12
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.39
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.57
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.16
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.50
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.92
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.16
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5192.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.38
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.27
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.92
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.38
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.84
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3955.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.13
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000130492

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.33
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999982214

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:02.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3997721.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  513.09
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.16
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.06
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908617
  j =  2                              :            45687
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.08
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.46
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.23
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.07
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.00
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.31
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.57
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.07
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.22
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.58
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5220.05
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.72
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.87e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9689.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.80
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5099.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.38
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999944684

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.91
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000001255

Normal statistic for number of bits   : 9.92e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:51.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5013529.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5546
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    3.19
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   40.25
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.07
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.01
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:24.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907846
  j =  2                              :            46074
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907796
  j =  2                              :            46090
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.27
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.39
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.36
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.66
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.82
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.49
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.44
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.57
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.43
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.56
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.37
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4642.84
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.19
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999867083

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.66
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999835076

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:26.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5963801.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9962


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7208.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4731.10
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907735
  j =  2                              :            46128
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908327
  j =  2                              :            45832
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17722.04
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.09
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.87
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.53
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.43
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5269.04
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.83
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.21
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.65
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.36
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000056107

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.58
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999901667

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:43.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7012377.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    3.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    3.53
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  515.35
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.16
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908514
  j =  2                              :            45734
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908229
  j =  2                              :            45869
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.50
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.51
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.18
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.17
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.32
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.47
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.31
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.08
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.36
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999940883

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.64
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999858197

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:29.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8028185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.94
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6831.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.47
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.11
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908875
  j =  2                              :            45558
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907888
  j =  2                              :            46047
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.26
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17860.87
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.58
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.60
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.72
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.98
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.18
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.40
p-value of test                       :    0.9942

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.00
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10312.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.98
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000085159

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.37
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999950483

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9011225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:16.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.52
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.62
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.58
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908018
  j =  2                              :            45985
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.22e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.82
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.12
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.90
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.83
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.95
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.43
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.87
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999956906

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.84
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000042916

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:43.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9961497.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    8.40
p-value of test                       :  7.7e-5    *****

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.23
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:28.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.45
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.98
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908453
  j =  2                              :            45763
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45446
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869446
  j =  1                              :        399909111
  j =  2                              :            45440
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.96e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.13
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.59
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.53
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.17
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.55
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 1.00e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11462.90
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.22
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999939059

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.25
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000183043

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:50.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3          7.7e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10977305.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:35.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    3.35
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.66
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908234
  j =  2                              :            45877
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46545
p-value of test                       :  9.7e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870545
  j =  1                              :        399906911
  j =  2                              :            46543
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.73
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.74
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.10
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.88
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3824.59
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.36
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000107161

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.18
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999968069

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.49
p-value of test                       :  6.3e-3

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 45  CollisionPermut, r = 10         9.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 97  HammingIndep, L=300, r=0        0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12025881.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.25
p-value of test                       :  8.0e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1544.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.07
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908704
  j =  2                              :            45642
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908386
  j =  2                              :            45804
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.54
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.12
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.67
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.62
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.13
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.65
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.28
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5216.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.87
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.91
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10295.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:29.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.84
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999928037

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000057322

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:30.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            8.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13041689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.88
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907981
  j =  2                              :            46005
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908803
  j =  2                              :            45591
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.30
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.79
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.08
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.73
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.85
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.69
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    6.93
p-value of test                       :  3.9e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -2.50
p-value of test                       :    0.9938

Sample variance                       :    4.08
p-value of test                       :  3.0e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.77e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.08
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.10
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12163.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.08
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000011386

Normal statistic for number of bits   :   0.090
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999840467

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:21.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13991961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5537
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9968

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9950


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.00
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.82
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.06
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907912
  j =  2                              :            46038
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908104
  j =  2                              :            45942
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.25
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17645.14
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.39
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.46
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.12
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.74
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.32
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.03
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.44
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:29.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.35
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999903371

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.22
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000104677

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:06.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14975001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7245.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.61
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:58.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908198
  j =  2                              :            45901
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907997
  j =  2                              :            45991
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.82
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.90
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.40
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.72
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.03
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.95
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.14
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.22
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.31
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:29.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4638.87
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.00
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.77
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000003106

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.95
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999967982

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    : 7.18e-5
p-value of test                       : 1 -  7.2e-5    *****

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.94
p-value of test                       :    0.9984

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:50.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15925265.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    3.76
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:37.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.91
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46288
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870288
  j =  1                              :        399907427
  j =  2                              :            46282
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.68
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.52
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.32
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.79
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.80
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.78
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.03
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.16
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000007735

Normal statistic for number of bits   :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.04
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999936725

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:42.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16842769.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.64
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.21
p-value of test                       :  2.6e-3

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.57
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.83
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46224
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870224
  j =  1                              :        399907554
  j =  2                              :            46220
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908788
  j =  2                              :            45600
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.80e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.63
p-value of test                       :  1.2e-4    *****

Anderson-Darling statistic = A2       :    8.29
p-value of test                       :  9.3e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :18193.04
p-value of test                       :  2.8e-5    *****



-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.90
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.97
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.34
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.34
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.29
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.32
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000189313

Normal statistic for number of bits   :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.43
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999901982

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:30.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 73  GCD                             2.8e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 94  HammingCorr, L = 1200           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17891345.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     818
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.75
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.98
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.38
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.01
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.58
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46477
p-value of test                       :  2.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870477
  j =  1                              :        399907052
  j =  2                              :            46465
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908527
  j =  2                              :            45735
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:10.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.01
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.96
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.59
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.05
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.97
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.13
p-value of test                       :  7.4e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.63
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.97
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11454.77
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.24
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000063541

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.74
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000019417

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.53
p-value of test                       :    0.9943

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:34.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19234833.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    4.71
p-value of test                       :  4.0e-3

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9939

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.55
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908771
  j =  2                              :            45610
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908527
  j =  2                              :            45735
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.52
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.46
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.54
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.18
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.35
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.17
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.66
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.86
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.96
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5108.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.05
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999977339

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.14
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999947291

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         : -6.04e-3
p-value of test                       :    0.50

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:27.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20152337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.50
p-value of test                       :  5.9e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    4.13
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9905


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.24
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.42
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907752
  j =  2                              :            46121
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908234
  j =  2                              :            45877
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.61
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.66
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4782.50
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.34
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.99
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.99
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.09
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.75
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.08
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000106033

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.46
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000129187

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:37.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           5.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 851994.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7224.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:50.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908465
  j =  2                              :            45757
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908537
  j =  2                              :            45727
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.46
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.25
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.43
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  182.05
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.40
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.21
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.22
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.45
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.33
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:31.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12092.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.74
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000038455

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.08
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999968984

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:37.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1441818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    3.17
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.56
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    4.49
p-value of test                       :  5.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.11
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:50.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908638
  j =  2                              :            45675
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908528
  j =  2                              :            45730
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.44e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17589.69
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.62
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.53
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.14
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.86
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.17
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000091477

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.92
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999907547

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:04.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2261018.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1327.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:53.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908249
  j =  2                              :            45871
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907994
  j =  2                              :            45997
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.44e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.11
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.99
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5202.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.48
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.80
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999980036

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.89
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999949742

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:35.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3375108.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46259
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870259
  j =  1                              :        399907483
  j =  2                              :            46257
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908701
  j =  2                              :            45648
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.56
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.63
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.64
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.13
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5214.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.26
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.41
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.34
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.62
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.31
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000127174

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.18
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999918644

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:43.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4521988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.29
p-value of test                       :  6.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    3.02
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.35
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908171
  j =  2                              :            45913
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908310
  j =  2                              :            45842
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:28.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.31
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.28
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.66
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.19
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.37
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.14
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.27
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.62
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.79
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.86
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.36
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.81
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.47
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000076642

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.12
p-value of test                       :  6.6e-3


-----------------------------------------------
Total number of bits:  7999894236

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:53.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5668868.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.46
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.36
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908277
  j =  2                              :            45857
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908238
  j =  2                              :            45872
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.00
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.13
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.97
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  7.8e-4    *****

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10339.24
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.92
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000130066

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.60
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999872000

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:28.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6586372.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7311.96
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  154.66
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.31
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907943
  j =  2                              :            46024
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908461
  j =  2                              :            45765
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.70
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17144.18
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.19
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.60
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.93
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.91
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5256.98
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.61
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.33
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.64
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.20
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10270.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.85
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.28
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000096991

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.08
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000087832

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7503876.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.57
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.93
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45494
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869494
  j =  1                              :        399909013
  j =  2                              :            45492
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908251
  j =  2                              :            45870
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.99
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.97
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.00
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.32
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.27
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.80
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.20
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.54
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    5.78
p-value of test                       :  1.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.37
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999812177

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.41
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999976025

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:22.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8519684.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.86
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908678
  j =  2                              :            45658
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46370
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870370
  j =  1                              :        399907261
  j =  2                              :            46368
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:15.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.35
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.65
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.49
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.37
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.20
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10232.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.58
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999933725

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.18
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999830609

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:27.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9568260.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.74
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.74
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907935
  j =  2                              :            46025
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908196
  j =  2                              :            45893
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17284.55
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.89
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.24
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.27
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.55
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.48
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.74
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.96
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000029656

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.57
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999935540

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10584068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.91
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.79
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5327.16
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908397
  j =  2                              :            45797
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908431
  j =  2                              :            45777
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  168.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16934.89
p-value of test                       :    0.9962



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.37
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.55
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.46
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.49
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.92
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.10
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.97
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.28
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999814913

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.00
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999857006

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:32.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11599876.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4182
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4778.45
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908523
  j =  2                              :            45734
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907927
  j =  2                              :            46035
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.68
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.17
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.74
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.30
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5248.35
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.16
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.54
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -401.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.16
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.14
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.79
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999975188

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.85
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000016606

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:13.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12615684.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.48
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.41
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908181
  j =  2                              :            45902
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908199
  j =  2                              :            45899
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.36e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -7.68e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.51
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.88
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.80
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.77
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.09
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4771.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.93
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.73
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.55
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:34.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.85
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000101362

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.41
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999963689

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:15.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13565956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.14
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908732
  j =  2                              :            45625
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.89
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.46
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.06
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.88
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.06
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.64
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.16
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:28.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.80
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.59
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999956276

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.20
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999945392

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:08.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14581764.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.01
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908210
  j =  2                              :            45889
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908830
  j =  2                              :            45579
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.22e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.33
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.85
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.93
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.69
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.55
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.54
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.84
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.30
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.13e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.30
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9768.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:28.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4298.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.07
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000014095

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.16
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999965663

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:43.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15597572.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9958

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9967

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.54
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.62
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.43
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45412
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869412
  j =  1                              :        399909178
  j =  2                              :            45408
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908557
  j =  2                              :            45714
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9924


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.15
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.60
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.77
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.57
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.99
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.48
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.82
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.00
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999971000

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000000943

Normal statistic for number of bits   : 7.46e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:16.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16613381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.77
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    5.20
p-value of test                       :  2.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.76
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.16
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907995
  j =  2                              :            45998
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.89e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.19
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.65
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.04
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.75
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.65
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000005680

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.52
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000140983

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:36.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17629189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5596
p-value of test                       :  9.1e-3


-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.25
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  498.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4837.41
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908050
  j =  2                              :            45972
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908043
  j =  2                              :            45968
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.58
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.20
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.86
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.61
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.79
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.31
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.46
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.15
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9722.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:32.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.30
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999991040

Normal statistic for number of bits   :  -0.071
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.93
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000010078

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:48.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18612229.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4902.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908293
  j =  2                              :            45849
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46307
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870307
  j =  1                              :        399907388
  j =  2                              :            46303
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.64e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.74
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.01
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.37
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  259.29
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.69
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.27
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.34
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.60
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:56.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  151.87
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.55
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.69
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000007897

Normal statistic for number of bits   :   0.062
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.95
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999967346

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:07.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19791877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     258
p-value of test                       :    0.9928

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:37.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7217.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.02
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907950
  j =  2                              :            46016
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908406
  j =  2                              :            45794
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.65e-4
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.09
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.26
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.09
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.83
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.25
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.14
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.31
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.13
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11515.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.48
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000006556

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.23
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999950660

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:06.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 884763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.68
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     665
p-value of test                       :  4.7e-3

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9954

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.09
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45496
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869496
  j =  1                              :        399909010
  j =  2                              :            45492
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    5.18
p-value of test                       :  2.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.78
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.92
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.56
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.30
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4727.14
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.26
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.96
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9672.36
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5036.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.78
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999985121

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.58
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999924041

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:17.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1736731.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     353
p-value of test                       :  1.5e-3

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.22
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.48
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46245
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870245
  j =  1                              :        399907514
  j =  2                              :            46237
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908040
  j =  2                              :            45965
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-6
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.90
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.11
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.88
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.11
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.26
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.51
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.50
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.78
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    2.55
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.32
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999970628

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.29
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999923321

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:01.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2687003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.25
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908570
  j =  2                              :            45709
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908461
  j =  2                              :            45765
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.35
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.60
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.40
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.76
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.64
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.27
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.66
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.81
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10257.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:30.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.42
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000040960

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000173077

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         : -4.38e-3
p-value of test                       :    0.50

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.13
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:15.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3473435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.47
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.95
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908591
  j =  2                              :            45703
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.73
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.86
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.30
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.34
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.53
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.25
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.73
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.45
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.78
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:30.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.55
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000035140

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.04
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999965081

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         : -7.98e-3
p-value of test                       :    0.50

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:55.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4456475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.91
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   82.47
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908857
  j =  2                              :            45561
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908530
  j =  2                              :            45732
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.76
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  208.20
p-value of test                       :  5.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.36
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.29
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.64
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.11
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9738.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:03:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000141910

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.80
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999910613

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:47.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     5.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5308443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1589.85
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.63
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.87
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908180
  j =  2                              :            45907
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908547
  j =  2                              :            45725
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17111.53
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.57
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.70
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.71
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.77
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.81
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.61
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   30.80
p-value of test                       :  1.5e-4    *****

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    6.76
p-value of test                       :  4.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  273.53
p-value of test                       :  4.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.35
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000099082

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999950645

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:08.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          1.5e-4
 88  PeriodsInStrings, r = 0         4.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6324251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.43
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45472
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869472
  j =  1                              :        399909061
  j =  2                              :            45462
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908923
  j =  2                              :            45534
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.56e-4
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    4.93
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   13.03
p-value of test                       : 1 -  9.0e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17113.10
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.07
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.06
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.25
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.25
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.47
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.44
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.06
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.52
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12267.23
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.80
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999947648

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.63
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999952655

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:02.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0           1 -  9.0e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7372827.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5553
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    4.89
p-value of test                       :  3.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     106
p-value of test                       : 1 -  9.4e-5    *****

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.45
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.10
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4874.40
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907920
  j =  2                              :            46037
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908194
  j =  2                              :            45897
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.56
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.61
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.16
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.77
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.07
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.44
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.72
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.83
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12277.89
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.04
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999968021

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   27.62
p-value of test                       :    0.9989


-----------------------------------------------
Total number of bits:  7999997154

Normal statistic for number of bits   :  -0.022
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16      1 -  9.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8388635.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997209
  j =  2                              :             1394
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.71
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.31
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.05
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908343
  j =  2                              :            45827
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908491
  j =  2                              :            45753
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.46e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.22
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.09
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.77
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.41
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.38
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.05
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12111.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.80
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999878834

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.54
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999962864

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9900

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Tests on the sum of all N observations
Standardized normal statistic         : -5.80e-3
p-value of test                       :    0.50

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:07.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9437211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.37
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.19
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.04
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908091
  j =  2                              :            45950
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908400
  j =  2                              :            45791
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.32e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.47
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.49
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.66
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.72
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.67
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:31.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.42
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999960419

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.34
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000062407

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:50.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10420251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4528
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4173
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    4.66
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   50.43
p-value of test                       :  6.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1344.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.20
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908239
  j =  2                              :            45876
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907715
  j =  2                              :            46129
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -7.23e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17644.43
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.32
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.39
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.48
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.82
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3928.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11564.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.21
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999858881

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.00
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000024658

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:36.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                6.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11468827.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5566
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.54
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.44
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908018
  j =  2                              :            45988
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908559
  j =  2                              :            45719
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.60e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17643.39
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.51
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.10
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.00
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.12
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.47
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.90
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.96
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:35.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5165.09
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.96
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.39
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000002188

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.16
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999952808

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:53.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12517403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.75
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908079
  j =  2                              :            45959
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908916
  j =  2                              :            45536
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17079.34
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.38
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.62
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.94
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.26
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.60
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5217.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.58
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.65
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.81
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.13
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000117322

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.26
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000024730

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:04.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13500443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.02
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.17
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.59
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908429
  j =  2                              :            45781
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907883
  j =  2                              :            46057
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.98e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  108.54
p-value of test                       :  1.0e-3    *****

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.58
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.73
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.41
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.67
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.18
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.87
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.56
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.04
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.87
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  265.90
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.26
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000069172

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.56
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999815381

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    2.57
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  3.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.20
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:31.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           1.0e-3
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14516251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.90
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.79
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45772
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869772
  j =  1                              :        399908458
  j =  2                              :            45768
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907756
  j =  2                              :            46113
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   15.03
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.08
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.91
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.38
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.59
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.16
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.91
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.83
p-value of test                       :  3.6e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:28.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12154.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.73
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000130828

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.44
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999949292

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:23.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15499291.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4493
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.44
p-value of test                       :  5.9e-3

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.75
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:59.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907773
  j =  2                              :            46112
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908368
  j =  2                              :            45813
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.05e-5
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.51
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.30
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.96
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.87
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.59
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.83
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.65
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.19
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-4
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.01
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.79
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:25.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.55
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000017338

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.24
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000046393

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:47.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16515099.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.48
p-value of test                       :  5.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.52
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.74
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.89
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908293
  j =  2                              :            45846
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908543
  j =  2                              :            45721
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:19.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.00e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:12.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.63
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.53
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.60
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.61
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.69
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.28
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.69
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9696.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:28.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.37
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000058957

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.29
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999979904

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:54.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17530907.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    7.00
p-value of test                       :  3.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.77
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46180
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870180
  j =  1                              :        399907641
  j =  2                              :            46178
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908242
  j =  2                              :            45873
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:12.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.19
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.62
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.24
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.33
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.23
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.73
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:30.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.92
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000084592

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000065350

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:13.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2S, t = 5         3.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18546715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7099
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.50
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5245.62
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908244
  j =  2                              :            45875
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45467
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869467
  j =  1                              :        399909068
  j =  2                              :            45463
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:18.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.093
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17253.69
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.68
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.63
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.87
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.74
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.37
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000020476

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.76
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000078913

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:16.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19562523.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    4.49
p-value of test                       :  5.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.26
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.37
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908242
  j =  2                              :            45873
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908156
  j =  2                              :            45913
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.08
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.92
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.13
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.50
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.34
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.15
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9967

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.13
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.89
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999779825

Normal statistic for number of bits   :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.88
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999890528

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.20
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:18.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 917532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.16
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.13
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.38
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907853
  j =  2                              :            46066
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908074
  j =  2                              :            45954
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.54
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.57
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17566.97
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.41
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.37
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.20
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.36
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.58
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.69
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.64
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:32.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4655.38
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.46
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999975932

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999966353

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:59.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1933340.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:38.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.23
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:57.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908736
  j =  2                              :            45623
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46069
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870069
  j =  1                              :        399907864
  j =  2                              :            46065
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.40
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.16
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  101.89
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.48
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.57
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:31.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.56
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000012088

Normal statistic for number of bits   :   0.096
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000066388

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.17
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:08.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2883612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  509.58
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6766.29
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.38
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46121
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870121
  j =  1                              :        399907762
  j =  2                              :            46113
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:27.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.89
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.89
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.16
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.83
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.30
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.25
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.32
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.57
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000101179

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.59
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999965201

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.90
p-value of test                       :  1.9e-3

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:48.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3702812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    5.12
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908303
  j =  2                              :            45847
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9937


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.74
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.95
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.33
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.10
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.21
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.30
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.96
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.65
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:31.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.82
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000066652

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.72
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999971477

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4653084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4191
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7564
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.13
p-value of test                       :  7.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.93
p-value of test                       :  9.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907917
  j =  2                              :            46034
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908490
  j =  2                              :            45746
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.05
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.70
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.91
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  421.46
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.53
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.25
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -403.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.04e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.57
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12121.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11516.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.82
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000146422

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.17
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999929150

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:10.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5341212.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.51
p-value of test                       :  5.2e-3

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.38
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.04
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908485
  j =  2                              :            45750
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46621
p-value of test                       :  2.8e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870621
  j =  1                              :        399906764
  j =  2                              :            46609
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.16e-5
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.25
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.73
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17641.39
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.86
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.20
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.91
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.13
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.23
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.35
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.45
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.74
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.88
p-value of test                       :  3.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.08
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999998957

Normal statistic for number of bits   : -8.25e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.92
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000095881

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:02.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 45  CollisionPermut, r = 10         2.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6553628.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1494
p-value of test                       :  2.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334614
  j =  1                              :        599997012
  j =  2                              :             1494
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  8.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.21
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.66
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5240.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45458
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869458
  j =  1                              :        399909089
  j =  2                              :            45448
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908186
  j =  2                              :            45901
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-4
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.51
p-value of test                       :  2.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.086
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.70
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.59
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.74
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.61
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.08
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.79
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.39
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11475.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.08
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999995792

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.61
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000162043

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:43.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           2.8e-4
 55  SampleCorr, k = 1               2.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7471132.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7344.41
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.94
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908524
  j =  2                              :            45732
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908620
  j =  2                              :            45684
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.99
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17130.99
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.59
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.09
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.45
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.98
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.37
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.04
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.68
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.65
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999838901

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.41
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999937118

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:30.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8486940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.83
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.82
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7313.16
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.25
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908054
  j =  2                              :            45970
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908790
  j =  2                              :            45602
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.23e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9950


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17142.35
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.93
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.59
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.10
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.69
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.04
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4685.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.47
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.59
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999967805

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.95
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999880766

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:52.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9502723.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    3.44
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.68
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:58.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908073
  j =  2                              :            45962
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907891
  j =  2                              :            46053
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.99
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   53.86
p-value of test                       :  4.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  418.17
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.15
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.22
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.33
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.15
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.49
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.04
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.74
p-value of test                       :    0.9969

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.33
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:31.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.69
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.55
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999832844

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.43
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999881135

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:33.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 R (L=50, r=25)      4.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10452995.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997195
  j =  2                              :             1401
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4496
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    5.31
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1523.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6810.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.66
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908555
  j =  2                              :            45721
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908125
  j =  2                              :            45936
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.36e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.48
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.22
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.17
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.44
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   47.15
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.68
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.82
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.37
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.84
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.80
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.47
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  294.18
p-value of test                       :  1.6e-5    *****


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5271.64
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.17
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.41
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.23
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.35
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12140.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12085.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.61
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999808919

Normal statistic for number of bits   :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.85
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999821108

Normal statistic for number of bits   :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:55.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    1.6e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11436035.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.09
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7242.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.27
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907944
  j =  2                              :            46022
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46364
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870364
  j =  1                              :        399907276
  j =  2                              :            46356
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.47e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:30.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.037
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.88
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.14
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.41
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.21
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.01
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10221.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.47
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000026389

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.49
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999990674

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:46.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12451843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.19
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.69
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908163
  j =  2                              :            45911
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.74
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.37
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.35
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.81
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.66
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -401.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9747.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 6.77e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:29.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.43
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999980009

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.16
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000114757

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.51
p-value of test                       :    0.9939

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13467651.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7225.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.59
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.02
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908878
  j =  2                              :            45558
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907751
  j =  2                              :            46123
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   87.17
p-value of test                       :  6.3e-6    *****

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.090
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17665.56
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.65
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.90
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.88
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.14
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.49
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.73
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:29.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999979145

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.91
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999827873

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:35.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            6.3e-6
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14483459.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.82
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.46
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    4.68
p-value of test                       :  4.1e-3

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.06
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.48
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5202.64
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46271
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870271
  j =  1                              :        399907463
  j =  2                              :            46261
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46189
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870189
  j =  1                              :        399907625
  j =  2                              :            46183
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.23
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.17
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.21
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.37
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.60
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.05
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.41
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10292.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:28.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.13
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000276718

Normal statistic for number of bits   :    2.19
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.57
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000071329

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:11.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15532035.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     540
p-value of test                       :    0.9931

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.36
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.98
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.70
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907780
  j =  2                              :            46104
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907918
  j =  2                              :            46035
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:19.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.69
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  203.30
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.93
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.21
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.85
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.44
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.71
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.64
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.42
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.88
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:26.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.92
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999979481

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.87
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000117826

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:00.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16547843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:31.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1337.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.49
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.16
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908209
  j =  2                              :            45891
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908083
  j =  2                              :            45954
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.59
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.59
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.84
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.76
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.55
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.23
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.35
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.21
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.12
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.93
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999974357

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.32
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999990512

Normal statistic for number of bits   :  -0.075
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         : -3.44e-3
p-value of test                       :    0.50

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17563651.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    3.37
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9944


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:37.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   24.23
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.85
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908540
  j =  2                              :            45724
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17179.74
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.36
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.75
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.22
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.24
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.16
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.42
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.75
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:28.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3955.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12167.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.88
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000163564

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.98
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000176656

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:59.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18677763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.58
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.57
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.83
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908830
  j =  2                              :            45576
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907688
  j =  2                              :            46153
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  2.4e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    4.89
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.9937

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.03e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.57
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.71
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.92
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.84
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4772.35
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.75
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.80
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.75
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.60
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.28
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.21
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12022.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999971963

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.48
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999923111

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.41
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:49.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19660803.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.75
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.28
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.59
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.24
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908341
  j =  2                              :            45825
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46119
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870119
  j =  1                              :        399907763
  j =  2                              :            46117
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.31
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.89
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.29
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.83
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.36
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.46
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.57
p-value of test                       :  2.3e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.48
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11558.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.22
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999996734

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.91
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999939980

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:37.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 950301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.92
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.73
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.54
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.98
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.98
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:46.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907848
  j =  2                              :            46073
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908870
  j =  2                              :            45562
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.83e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.69
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.13
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.62
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.02
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.59
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.71
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:34.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.57
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.85
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999970901

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.50
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000160774

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:30.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1474589.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9934

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.10
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.39
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908317
  j =  2                              :            45837
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908046
  j =  2                              :            45974
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.10
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17013.15
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.33
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.01
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.08
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.07
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5216.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.63
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.49
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.11
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.48
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.71
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.69
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11544.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.94
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999973916

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.00
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999970235

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:57.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2228253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:36.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:54.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908619
  j =  2                              :            45683
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908599
  j =  2                              :            45696
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17337.68
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.75
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.42
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.13
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.10
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.08
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.32
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.02
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.58
p-value of test                       :    0.9913

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:31.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.59
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000115009

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999890711

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:09.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3309597.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9967

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.50
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.30
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907828
  j =  2                              :            46077
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907971
  j =  2                              :            46004
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.00
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.97
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.01
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.14
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.00
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.98
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.51
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.58
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.84
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:35.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.03
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999992903

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.95
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000095680

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:18.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4292637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.62
p-value of test                       :  4.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  524.15
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.16
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908301
  j =  2                              :            45842
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.56e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.93
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.35
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.63
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.82
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -4.96e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11420.00
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.83
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999991361

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999967166

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:37.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5472285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7610
p-value of test                       :  3.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7520
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7063
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9978


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  506.93
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.30
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4870.31
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908338
  j =  2                              :            45828
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908047
  j =  2                              :            45972
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.88e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.78e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.32
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.95
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.36
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.91
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.18
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.82
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.06
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.34
p-value of test                       :  9.1e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11524.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.73
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000105667

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.52
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000115345

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:06.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 15  BirthdaySpacings, t = 4         3.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6389789.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    3.91
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46304
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870304
  j =  1                              :        399907398
  j =  2                              :            46292
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908413
  j =  2                              :            45789
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.02
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.65
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.75
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.20
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4722.85
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.54
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.38
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.19
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5094.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12185.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.94
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999949796

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.82
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999940730

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:38.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7405573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    5.35
p-value of test                       :  2.0e-3

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.62
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.63
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45546
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869546
  j =  1                              :        399908914
  j =  2                              :            45534
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45571
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869571
  j =  1                              :        399908862
  j =  2                              :            45563
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17039.48
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.59
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.63
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.24
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.63
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.14
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.34
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.70
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.95
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.43
p-value of test                       :  7.5e-3

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.77
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:31.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.47
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.07
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999851312

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.73
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000104314

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:29.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8454149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5551
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9910

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.65
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7185.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.78
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908128
  j =  2                              :            45933
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908972
  j =  2                              :            45511
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.9903

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -3.66
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.12
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.77
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.57
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.45
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.43
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.08
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.85
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000056494

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.19
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000224383

Normal statistic for number of bits   :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:36.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9469957.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7538
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  355.82
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.78
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.16
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.39
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908063
  j =  2                              :            45958
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908415
  j =  2                              :            45788
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.36
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.32
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.24
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.44
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.94
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.38
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.76
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.14
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:31.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999942344

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.80
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999884618

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.72
p-value of test                       :  3.2e-3

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:29.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10551301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.29
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.45
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.77
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908141
  j =  2                              :            45919
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46162
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870162
  j =  1                              :        399907681
  j =  2                              :            46152
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17776.70
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.84
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.96
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.78
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.96
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.25
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.93
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.04
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000121888

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.81
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999943262

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:19.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11730949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.12
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908082
  j =  2                              :            45953
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908279
  j =  2                              :            45859
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.31
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.52
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.89
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.76
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.67
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.37
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.97
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.90
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.60
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9908

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.09
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:30.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5107.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.61
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.92
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000124183

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000035473

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.58
p-value of test                       :  4.9e-3

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:51.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12550149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.19
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.68
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:10.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908720
  j =  2                              :            45634
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908262
  j =  2                              :            45860
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17754.41
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.31
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.47
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.56
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.86
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:30.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.15
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000122998

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.32
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000079318

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         : 8.08e-3
p-value of test                       :    0.50

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:21.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13533189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7095
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6881.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.36
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908585
  j =  2                              :            45694
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908231
  j =  2                              :            45880
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9903


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:19.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.52
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17337.16
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.48
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.23
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.72
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.76
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.87
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9691.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.32
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999941486

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.19
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999917591

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:23.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14548997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.98
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.48
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908786
  j =  2                              :            45604
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908002
  j =  2                              :            45999
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9924


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.67
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.47
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.16
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.15
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.32
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.16
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.25
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.90
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.55
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.97
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:32.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5138.21
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.07
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000008530

Normal statistic for number of bits   :   0.067
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.80
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000093937

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:53.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15564805.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.42
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.97
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.57
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907893
  j =  2                              :            46046
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45496
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869496
  j =  1                              :        399909013
  j =  2                              :            45486
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.65
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.62
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.39
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.38
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.18
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.97
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.91
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.77
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4325.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.14
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999950867

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.50
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999970838

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:33.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16580612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4204
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.05
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.55
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.33
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908746
  j =  2                              :            45621
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908395
  j =  2                              :            45798
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 3.68e-4
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 1.53e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.01
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.75
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.84
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.29
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.11
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.94
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:28.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.88
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999964262

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.04
p-value of test                       :  8.2e-3


-----------------------------------------------
Total number of bits:  8000116041

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:55.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17596420.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7413.76
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.89
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4830.06
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45607
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869607
  j =  1                              :        399908787
  j =  2                              :            45605
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-4
p-value of test                       :  1.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.86e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    6.91
p-value of test                       :  3.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.71
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.69
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.54
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.01
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.87
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  311.54
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.87
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10237.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    6.77
p-value of test                       :  4.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4615.65
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.45
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999995024

Normal statistic for number of bits   :  -0.039
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.11
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000022435

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:33.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               3.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18579460.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  174.62
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   17.72
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.66
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4879.75
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46374
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870374
  j =  1                              :        399907255
  j =  2                              :            46368
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45495
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869495
  j =  1                              :        399909010
  j =  2                              :            45495
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.58e-4
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:19.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:12.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.43
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.61
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.52
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.46
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.53
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.74
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.45
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.57
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999939302

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.61
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999842357

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:08.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19628036.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:26.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.32
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.25
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908243
  j =  2                              :            45871
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908397
  j =  2                              :            45800
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.31e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.49
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.96
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  588.85
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.67
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.68
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.48
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.06
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.38
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.23
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.15
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10375.76
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.51
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000060037

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.90
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999940544

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:54.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 983070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.08
p-value of test                       :  8.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:32.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.37
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.84
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.58
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907798
  j =  2                              :            46098
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907802
  j =  2                              :            46090
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.79
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.93
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.16
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.56
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.47
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.69
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.37
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.15
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000041902

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.48
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000031678

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:56.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1605662.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4165
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    4.35
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:47.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45524
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869524
  j =  1                              :        399908956
  j =  2                              :            45516
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908224
  j =  2                              :            45882
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.13
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17826.45
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.24
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.85
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.08
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.28
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.89
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10256.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:35.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4688.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4308.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.05
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000072970

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999966425

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:44.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2129926.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    3.11
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.17
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.02
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908362
  j =  2                              :            45816
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908436
  j =  2                              :            45773
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.9903

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.25e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.93e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.67
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.49
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.60
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.01
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.42
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.57
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.03
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.79
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.17
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999993791

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.16
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000065587

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:15.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3244038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7549
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.79
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.86
p-value of test                       :  1.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.78
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6941.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.28
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907852
  j =  2                              :            46065
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908621
  j =  2                              :            45688
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.56
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.66
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.09
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.73
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.80
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.31
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.01
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.85
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.05
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999874730

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.77
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999851828

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:21.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4227078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.62
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.26
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.65
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908039
  j =  2                              :            45976
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908586
  j =  2                              :            45698
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.8e-3

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.96
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.77
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.59
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.80
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.13
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.84
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.01
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.26
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    2.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:30.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5063.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12139.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.25
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999859151

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.21
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000067090

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:46.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5242886.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:31.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.95
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4866.88
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908179
  j =  2                              :            45900
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907753
  j =  2                              :            46116
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.093
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.19
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.98
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.19
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.75
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.35
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.10
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.53
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.84
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -401.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.05
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:29.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.42
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999969968

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.04
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000061057

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:04.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6193158.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1483
p-value of test                       :  7.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334603
  j =  1                              :        599997034
  j =  2                              :             1483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    3.76
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     996
p-value of test                       :  8.6e-4    *****

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.37
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4874.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908179
  j =  2                              :            45903
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17888.75
p-value of test                       :  7.4e-3



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.78
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.62
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.27
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.57
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.88
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.72
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:27.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.47
p-value of test                       :  6.2e-3


-----------------------------------------------
Total number of bits:  7999954635

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000101779

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:48.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.8e-4
 22  ClosePairs NJumps, t = 3        8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7176198.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997263
  j =  2                              :             1367
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    4.75
p-value of test                       :  3.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     356
p-value of test                       :  9.0e-4    *****

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.80
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46401
p-value of test                       :  7.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870401
  j =  1                              :        399907201
  j =  2                              :            46395
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:12.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.31
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.35
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.28
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.68
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.89
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.18
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.10
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.71
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:27.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.79
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999957410

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.28
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000132343

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:57.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NJumps, t = 9        9.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8126470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.18
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908500
  j =  2                              :            45747
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908452
  j =  2                              :            45765
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:19.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:29.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.77
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.40
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.51
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  462.06
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.46
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.94
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.77
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:28.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.35
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999950420

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.19
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999981890

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:49.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9142278.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1233
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334353
  j =  1                              :        599997534
  j =  2                              :             1233
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     657
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6873.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.38
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:55.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907952
  j =  2                              :            46021
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908718
  j =  2                              :            45635
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.09e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:18.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:12.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:29.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.71
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.86
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.90
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.79
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.87
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.77
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.97
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.05
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.09
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:24.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.07
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999947816

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.05
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999961676

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:11.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10158086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4189
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9912


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.32
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.90
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907715
  j =  2                              :            46135
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908989
  j =  2                              :            45504
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:12.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.54
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.18
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.84
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.87
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.65
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.82
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.96
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.00
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.69
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999922475

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.33
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000232003

Normal statistic for number of bits   :    1.83
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.66
p-value of test                       :  3.9e-3

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:09.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11173894.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:31.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.72
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  168.06
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  362.42
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.42
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.14
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:49.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908832
  j =  2                              :            45575
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908421
  j =  2                              :            45782
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:14.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.20
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.52
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.89
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.37
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.85
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.54
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.97
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10209.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10376.16
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.90
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000004942

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.13
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000038731

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:38.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12189702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:31.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4148
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.01
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5228.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907845
  j =  2                              :            46064
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908616
  j =  2                              :            45686
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.73
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.92
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.25
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.56
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.68
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.70
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.38
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.00
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.01
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.72
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.98
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.35
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.51
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000019333

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000092785

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:01.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13205510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:34.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.00
p-value of test                       :  8.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    5.21
p-value of test                       :  2.3e-3

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    3.10
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6887.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.73
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.80
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908359
  j =  2                              :            45816
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908385
  j =  2                              :            45803
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.34
p-value of test                       :  2.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17216.56
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.35
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.74
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.09
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.63
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.50
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.09
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4345.96
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.94
p-value of test                       :    0.9927


-----------------------------------------------
Total number of bits:  8000017983

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.60
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999832814

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:11.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14221318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4495
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     662
p-value of test                       :  6.6e-3

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.23
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908468
  j =  2                              :            45763
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908219
  j =  2                              :            45883
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.57e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:12.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17121.39
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.86
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.00
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.95
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.07
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.45
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.93
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.03
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.18
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.82
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:28.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5113.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4295.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.50
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999955187

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.55
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999847358

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:01.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15237126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5264
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.17
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.60
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908225
  j =  2                              :            45880
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908217
  j =  2                              :            45890
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.21

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.88e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:19.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.14
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.79
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.06
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.61
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.47
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.93
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  445.29
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.28
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.32
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:25.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11506.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.32
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000076045

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.80
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000037369

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:34:58.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16252934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    3.69
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.94
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    6.76
p-value of test                       :  4.4e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.08
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.37
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46375
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870375
  j =  1                              :        399907254
  j =  2                              :            46367
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908581
  j =  2                              :            45702
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.39
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17776.63
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.92
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.79
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:21.45

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.17
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.31
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999982838

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.70
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999882401

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:43.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         4.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17268742.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     992
p-value of test                       :  1.3e-3

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1332.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.85
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.50
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.45
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46255
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870255
  j =  1                              :        399907499
  j =  2                              :            46237
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908848
  j =  2                              :            45567
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:19.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.03

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.84
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.91
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.69
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.54
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.09
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.80
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5132.41
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.57
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000100840

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.15
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000029599

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:40.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18284550.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n85, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    3.60
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    3.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.81
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.30
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45517
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869517
  j =  1                              :        399908973
  j =  2                              :            45503
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n85, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908488
  j =  2                              :            45753
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:19.23

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:12.80

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:29.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:29.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.73
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.16
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.41
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.41
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.49
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10252.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11481.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.41
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000103027

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.83
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999874385

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n85, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:35:04.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19300358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.71
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.43
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908217
  j =  2                              :            45884
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908145
  j =  2                              :            45920
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:19.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17646.89
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5303.56
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.85
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.36
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.70
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.41
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.76
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.96
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  147.59
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:35.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11471.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.56
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000000790

Normal statistic for number of bits   : 6.25e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.17
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999863159

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:54.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 0.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.44
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4707.49
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908814
  j =  2                              :            45593
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908747
  j =  2                              :            45619
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.96
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.21
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.90
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.05
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.00
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.14
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.72
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.59
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.58
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.63
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:30.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.39
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999815210

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.95
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999904865

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:33.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1671196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:34.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.36
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:49.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908043
  j =  2                              :            45974
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908706
  j =  2                              :            45644
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.29e-5
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17265.26
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.09
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.70
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.48
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.42
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.58
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.01
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.95
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -6.15e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:30.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  3.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.14
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000087541

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.53
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000093013

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:15.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2523163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.74
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:33.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6839.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.37
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:47.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45626
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869626
  j =  1                              :        399908748
  j =  2                              :            45626
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908408
  j =  2                              :            45796
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.72
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.53
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.44
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.10
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.48
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.43
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.46
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.20
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.83
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -401.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.86
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.86
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12129.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.85
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999918212

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.73
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000109327

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:17.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3342350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997209
  j =  2                              :             1394
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.54
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.72
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.24
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5211.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908335
  j =  2                              :            45828
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908052
  j =  2                              :            45971
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-4
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.97
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.05
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.43
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  144.07
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.31
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.67
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12088.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.12
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999957794

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.90
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999938801

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:28.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4194318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9987

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.68
p-value of test                       :  4.3e-3

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    4.38
p-value of test                       :  5.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7272.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:31.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.43
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908352
  j =  2                              :            45821
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908408
  j =  2                              :            45787
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.63
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.26
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.24
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.10
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.66
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.56
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.75
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.02
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:31.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11480.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.82
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999804149

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.87
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999956579

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.4e-4    *****

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.72
p-value of test                       :  3.3e-3

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:55.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5210126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997345
  j =  2                              :             1326
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1492
p-value of test                       :  3.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334612
  j =  1                              :        599997016
  j =  2                              :             1492
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.69
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5277.00
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908261
  j =  2                              :            45868
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45458
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869458
  j =  1                              :        399909089
  j =  2                              :            45448
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.55
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.77
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.60
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  534.66
p-value of test                       :  5.4e-7    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  474.14
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.23
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.94
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.12
p-value of test                       :  5.3e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.48
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.85
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.22
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.07
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999994172

Normal statistic for number of bits   :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.66
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000066976

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:04.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            3.4e-4
 79  RandomWalk1 H (L=10000, r=15)   5.4e-7
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6455309.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.96
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.97
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907888
  j =  2                              :            46050
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46324
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870324
  j =  1                              :        399907355
  j =  2                              :            46318
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.39
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.24
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.88
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.12
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.79
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.30
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.49
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.55
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.57
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.53
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999966617

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.16
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000001660

Normal statistic for number of bits   :   0.013
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:20.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7438349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7556
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.07
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.34
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.69
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:52.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908702
  j =  2                              :            45640
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907951
  j =  2                              :            46017
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17845.53
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.10
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.88
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.22
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.03
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.37
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.25
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.66
p-value of test                       :  8.6e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.04
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.59
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:30.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.96
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000088249

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000055822

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         : 7.10e-3
p-value of test                       :    0.50

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:21.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8454157.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1230
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334350
  j =  1                              :        599997540
  j =  2                              :             1230
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9904


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7275.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.89
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:51.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908578
  j =  2                              :            45705
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908084
  j =  2                              :            45949
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.73
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17554.30
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.71
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.13
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.22
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.46
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.58
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.70
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.87
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.07
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -401.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.11
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.41
p-value of test                       :    0.9941

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10323.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999898712

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.57
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000078208

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:26.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9437197.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5294
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9905

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9937


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.07
p-value of test                       :  8.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.75
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.08
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907901
  j =  2                              :            46045
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907720
  j =  2                              :            46134
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.02e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.67
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.67
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.61
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.53
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.84
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.50
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.29
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.43
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.55
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.29
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.32
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:35.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4336.39
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.72
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999890312

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.30
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999999980

Normal statistic for number of bits   : -1.58e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.14
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:55.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10747917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.82
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4868.70
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46278
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870278
  j =  1                              :        399907447
  j =  2                              :            46272
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907974
  j =  2                              :            46007
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.36
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.06
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.96
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.27
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.72
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.96
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.33
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.88
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11495.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.15
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999987854

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.00
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000028192

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:51.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11763725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9938

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.59
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:45.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908419
  j =  2                              :            45783
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907780
  j =  2                              :            46104
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17232.71
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.65
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.73
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.28
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.89
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.46
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5202.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.16
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.03
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000012751

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.92
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999912044

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:13.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12713997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9994    *****

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46262
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870262
  j =  1                              :        399907480
  j =  2                              :            46254
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46478
p-value of test                       :  2.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870478
  j =  1                              :        399907052
  j =  2                              :            46462
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.41e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.58
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.26
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.57
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.64
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.94
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.00
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.56
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.27
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.02
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.05
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9700.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.66
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000052597

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999955760

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:30.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13697037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1216
p-value of test                       : 1 -  2.3e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334336
  j =  1                              :        599997568
  j =  2                              :             1216
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9912


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:30.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.46
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908528
  j =  2                              :            45730
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907677
  j =  2                              :            46157
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.16e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.82
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.47
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.03
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.92
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.46
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.88
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.19
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:29.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.13
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999902816

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.17
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000094924

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:03.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14          1 -  2.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14745613.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9935

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:38.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.71
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4827.67
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:55.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907861
  j =  2                              :            46068
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908205
  j =  2                              :            45890
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.43
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.70
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.77
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.32
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.06
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:29.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5142.28
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.63
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000005533

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.43
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999989069

Normal statistic for number of bits   :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15532045.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:37.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.70
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4828.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908293
  j =  2                              :            45849
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17178.65
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.95
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.31
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.91
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.49
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:29.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5122.09
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.86
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999895952

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.03
p-value of test                       :  4.5e-3


-----------------------------------------------
Total number of bits:  7999856574

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:58.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16515085.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    3.44
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    4.47
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.18
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908581
  j =  2                              :            45702
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908002
  j =  2                              :            45996
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.44
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.10
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.62
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.56
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.99

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.05
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10348.48
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:32.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999954956

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.87
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999989918

Normal statistic for number of bits   :  -0.080
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17530893.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7078
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1599.88
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.18
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.10
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908266
  j =  2                              :            45858
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908196
  j =  2                              :            45896
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.49
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.17
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.21
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.44
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.79
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.98
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.33
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.56
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.60
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.06
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:28.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.09
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999980276

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.34
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000031882

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:20.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18546701.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.21
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.68
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.33
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908386
  j =  2                              :            45804
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908010
  j =  2                              :            45986
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:19.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17553.54
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.75
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.88
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.51
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.95
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.21
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  257.54
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.37
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.92
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.94
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:26.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.35
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5118.07
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.42
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000062347

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.28
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000058198

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:49.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19562509.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  179.97
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7217.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.91
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.18
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:54.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907987
  j =  2                              :            46002
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907797
  j =  2                              :            46100
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17360.06
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.79
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.62
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.69
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000056431

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.19
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000026452

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:34.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 32769.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.70
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9967

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907962
  j =  2                              :            46013
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45574
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869574
  j =  1                              :        399908854
  j =  2                              :            45570
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:27.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.69
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.68
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.86
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.07
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.40
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.58
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.80
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.41
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.45
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.54
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.79
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000083788

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.35
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000059647

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:45.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1900545.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7561
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:35.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.13
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.45
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908534
  j =  2                              :            45724
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908679
  j =  2                              :            45653
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.37
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.62
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.23
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.50
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10225.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.97
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12094.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.80
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000104632

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.88
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999823784

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2850817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.61
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4877.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908533
  j =  2                              :            45732
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907707
  j =  2                              :            46145
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  8.3e-4    *****

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.66
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.34
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.76
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.18
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.12
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.94
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.86
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.69
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.36
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.65
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4349.79
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12136.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.65
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000062503

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.38
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000055249

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.41
p-value of test                       :  7.9e-3

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:58.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3866625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.72
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6819.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.96
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908368
  j =  2                              :            45813
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908247
  j =  2                              :            45869
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.08e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:29.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.43
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.67
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.12
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.57
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.00
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.50
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.92
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.18
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999984515

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.08
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000014935

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         : -1.98e-3
p-value of test                       :    0.50

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:40.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4784129.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997235
  j =  2                              :             1381
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:33.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.64
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1559.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.82
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.90
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907643
  j =  2                              :            46177
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908245
  j =  2                              :            45873
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17618.03
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.89
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.12
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.38
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.37
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5212.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.93
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.09
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.37
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.84
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.63
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000110566

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.35
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000050863

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.41
p-value of test                       :  8.0e-3

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:30.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5799937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.52
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.57
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.12
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908114
  j =  2                              :            45934
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907837
  j =  2                              :            46077
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9987


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 4.03e-4
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    5.18
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.30
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.19
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.52
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.58
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.30
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.00
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.94
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.90
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.83
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.69
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999893300

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000020410

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:48.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6815745.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.72
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908188
  j =  2                              :            45900
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908200
  j =  2                              :            45897
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.67
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.66
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.88
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.43
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.29
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.98
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.22
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.87
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.83
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.62
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.03
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.91
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:32.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12086.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.17
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000103759

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.86
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000060403

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:16.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7798785.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9953


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.01
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.04
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908094
  j =  2                              :            45950
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908357
  j =  2                              :            45814
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  6.5e-4    *****

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-4
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.38e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17266.16
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.09
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.61
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.80
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.88
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12116.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.98
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999935141

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.68
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000057952

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8847361.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5534
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.83
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.05
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908037
  j =  2                              :            45977
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908628
  j =  2                              :            45680
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 4.00e-4
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.87
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.16
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.04
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.60
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.70
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.73
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999951113

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.63
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000099910

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9863169.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:30.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.55
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46303
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870303
  j =  1                              :        399907397
  j =  2                              :            46297
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907932
  j =  2                              :            46028
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.50e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.87
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.80
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
p-value of test                       : 1 -  5.0e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  192.44
p-value of test                       :  3.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17714.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.21
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  186.54
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.65
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.38
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.42
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.44
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.53
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.83
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.26
p-value of test                       :    0.9960

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.26
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999905636

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.53
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000204175

Normal statistic for number of bits   :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          3.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10846209.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.28
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908524
  j =  2                              :            45738
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908629
  j =  2                              :            45684
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.21e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.54
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.42
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.21
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.91
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.30
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.07
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.83
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.12
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.48
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.80
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:34.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.56
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12222.30
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.80
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999974747

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.44
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000135022

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:40.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11862017.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4162
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:47.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:28.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:28.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.31
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.40
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907884
  j =  2                              :            46052
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908687
  j =  2                              :            45652
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.67
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.80
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.74
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.05
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.45
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:28.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.44
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000036442

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.43
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999913220

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:14.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12910593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6810.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5144.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:00.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908689
  j =  2                              :            45651
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908296
  j =  2                              :            45843
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.70
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.16
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.27
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.32
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.80
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.61
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.72
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-5
p-value of test                       : 1 -  1.0e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.93
p-value of test                       :  1.7e-3

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.63
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10277.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:28.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.86
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000026389

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.97
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000000889

Normal statistic for number of bits   : 7.03e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:59.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14155777.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    3.55
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:49.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.58
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   91.67
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.23
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.99
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907851
  j =  2                              :            46073
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908888
  j =  2                              :            45550
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:14.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.92
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.73
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.47
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.51
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.90
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.54
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.06
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.53e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:33.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.74
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999992936

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.55
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000112570

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.019
p-value of test                       :    0.49

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:29.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15171585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5260
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    6994
p-value of test                       : 1 -  6.9e-5    *****


-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:46.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.00
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.73
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.58
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909126
  j =  2                              :            45434
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908440
  j =  2                              :            45774
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  8.6e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.59e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 4.77e-4
p-value of test                       :  1.1e-4    *****

Anderson-Darling statistic = A2       :    5.06
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16990.00
p-value of test                       :    0.9912



-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.41
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.32
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.00
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.56
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.70
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.46
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.86
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.76
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.54
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3951.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.08
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999901535

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.79
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999997943

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:43.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16       1 -  6.9e-5
 47  MaxOft, t = 16                  8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16187393.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:52.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.23
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.06
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:55.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45466
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869466
  j =  1                              :        399909071
  j =  2                              :            45460
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908515
  j =  2                              :            45741
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.43
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.59
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.02
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.33
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.16
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.72
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5201.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.89
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.49
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4784.84
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.01
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.70
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    4.30
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4610.71
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.10
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000009877

Normal statistic for number of bits   :   0.078
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.01
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999990785

Normal statistic for number of bits   :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:31.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17203201.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:47.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:24.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:49.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.78
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:52.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46173
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870173
  j =  1                              :        399907657
  j =  2                              :            46167
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908533
  j =  2                              :            45726
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.04
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.27
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.36
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.65
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.10
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.01
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.47
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4797.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.26
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.19
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.52
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12086.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999906605

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000014953

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:47.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18186241.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:20.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:47.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7200.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.19
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.04
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:55.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908853
  j =  2                              :            45569
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908250
  j =  2                              :            45869
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.73
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.49
p-value of test                       :    0.9901


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   65.71
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.77
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.57
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.57
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.64
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.08
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.98
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:28.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.52
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.99
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999994679

Normal statistic for number of bits   :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.40
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000105817

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:08.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19267585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    4.84
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:02:16.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:51.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.87
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.26
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908005
  j =  2                              :            45993
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908300
  j =  2                              :            45847
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.37
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.97
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.12
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.24
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.62
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.00
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.47
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.04
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.86
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.10
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10394.87
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9630.57
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:20.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.90
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000038575

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.79
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999846323

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    2.81
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:29.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20283393.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5589
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.92
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.11
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  183.74
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.49
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908185
  j =  2                              :            45906
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908812
  j =  2                              :            45588
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:19.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.16
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.78
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.50
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.22
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.24
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.38
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.96
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.60
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.71
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999859541

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.86
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000050578

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:33.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 65538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.24
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.77
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.08
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908539
  j =  2                              :            45726
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907781
  j =  2                              :            46105
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17911.22
p-value of test                       :  5.3e-3



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.90
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.48
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.63
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.09
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.04
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.30
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.63
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999815312

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000112459

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:01.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1441794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.80
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9955

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.00
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907884
  j =  2                              :            46052
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45406
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869406
  j =  1                              :        399909192
  j =  2                              :            45398
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:27.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.57
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.22
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.44
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.63
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.04
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.37
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.29
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.20
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9709.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.82
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000041059

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.78
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999937451

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:54.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2195467.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9945


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:46.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.96
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907800
  j =  2                              :            46097
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908744
  j =  2                              :            45622
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.78
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.70
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.97
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.27
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.30
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.70
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999840974

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.31
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999989369

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.70
p-value of test                       :    0.9965

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:00.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3899403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9984

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.97
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.24
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908426
  j =  2                              :            45775
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908098
  j =  2                              :            45945
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.50
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.26
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.09
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.32
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.80
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.04
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4764.97
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.32
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.31
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.39
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.72
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000009028

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.48
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000120031

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:42.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4816907.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    4.44
p-value of test                       :  5.3e-3

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.47
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908211
  j =  2                              :            45893
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908093
  j =  2                              :            45946
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.95e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -8.99e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.24
p-value of test                       :  5.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.90
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.15
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.84
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.33
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.40
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4765.88
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.93
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.07
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10332.25
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.78
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000066730

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.23
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999995249

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  9.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:41.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 58  AppearanceSpacings, r = 27      5.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5832715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:46.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  283.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.66
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.54
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908162
  j =  2                              :            45913
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908222
  j =  2                              :            45880
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:09.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.97
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.86
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.37
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.41
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.51
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.35
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999992525

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.30
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000108457

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:05.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6881291.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.77
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.98
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.53
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46175
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870175
  j =  1                              :        399907656
  j =  2                              :            46163
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908525
  j =  2                              :            45730
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17752.19
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.76
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.65
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.92
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.99
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.14
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.33
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.53
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999898076

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.04
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999965786

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:38.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7864331.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    4.81
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:45.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.12
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:46.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45278
p-value of test                       :    0.9975


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869278
  j =  1                              :        399909445
  j =  2                              :            45276
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908127
  j =  2                              :            45929
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.04
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.14
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.58
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.29
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.80
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.17
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.06
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4600.46
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.36
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000158122

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999951113

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.15
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:14.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8814603.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5589
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.67
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.94
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.23
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46213
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870213
  j =  1                              :        399907578
  j =  2                              :            46205
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.64e-6
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.24
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.28
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.57
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.34
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5249.10
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.06
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9713.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.90
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000144508

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.16
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999900908

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    2.67
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.095
p-value of test                       :    0.54

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9732107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       : 1 -  3.6e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997265
  j =  2                              :             1366
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1562.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.08
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:47.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907872
  j =  2                              :            46061
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908484
  j =  2                              :            45755
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.88
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.89
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.46
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.76
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.17
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.51
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.64
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.06
p-value of test                       :    0.9993    *****


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.77
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:31.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.09
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000251911

Normal statistic for number of bits   :    1.99
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000113866

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:27.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22             1 -  3.6e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 81  LinearComp, r = 0               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10551307.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:39.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.16
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.75
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908134
  j =  2                              :            45924
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908635
  j =  2                              :            45675
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -3.25e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:27.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.030
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17643.57
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   95.18
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.15
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.83
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4707.22
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.52
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.18
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.72
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.97
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.74
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.27
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.29
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.16
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.33
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000006952

Normal statistic for number of bits   :   0.055
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.49
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000057805

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:11.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11730955.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4505
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.95
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.52
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:51.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908725
  j =  2                              :            45636
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908226
  j =  2                              :            45887
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17524.98
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.94
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.00
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.50
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.32
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.54
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.15
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.90
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9697.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:29.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12120.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.44
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000005941

Normal statistic for number of bits   :   0.047
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.19
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999996794

Normal statistic for number of bits   :  -0.025
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:25.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12648459.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4177
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.67
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.41
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:52.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46250
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870250
  j =  1                              :        399907503
  j =  2                              :            46244
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908247
  j =  2                              :            45872
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17216.88
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   49.10
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.98
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.17
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.13
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.91
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.66
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  451.73
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.04
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -401.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.33
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.92
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:30.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4276.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11299.36
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.26
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000097333

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000050257

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    5.98
p-value of test                       :  1.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.40
p-value of test                       :    0.9997    *****

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:12.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 99  HammingIndep, L=1200, r=0       0.9997 
 106  AutoCor, d=3, r=27              0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13664267.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.66
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6849.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.15
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4846.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908294
  j =  2                              :            45850
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908535
  j =  2                              :            45725
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.81
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.50
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.95
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.75
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.81
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.01
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000051055

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999915641

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.032
p-value of test                       :    0.49

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14549003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5269
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    4.04
p-value of test                       :  8.3e-3

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    3.83
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.71
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.09
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.03
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907815
  j =  2                              :            46079
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907975
  j =  2                              :            46011
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.21
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.92
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.84
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.72
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.36
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.20
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.18
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.68
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.40
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:29.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5136.76
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.97
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000026086

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.35
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000026797

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:38.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15499275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     831
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.90
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.87
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45617
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869617
  j =  1                              :        399908772
  j =  2                              :            45605
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45335
p-value of test                       :    0.9945


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869335
  j =  1                              :        399909336
  j =  2                              :            45323
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.03
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.44
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.67
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.33
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.09
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.47
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  425.56
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.81
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.74
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    5.48
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.23
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.50
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.47
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.83
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4307.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.57
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.02
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999972119

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999996974

Normal statistic for number of bits   :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.12
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:48.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16547851.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:46.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.43
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:19.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.96
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908439
  j =  2                              :            45773
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908088
  j =  2                              :            45947
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.44
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.98
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17607.20
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.87
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.85
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.49
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.36
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.06
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000052603

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.09
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000043231

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18022423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9912

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.74
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.30
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907849
  j =  2                              :            46071
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46152
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870152
  j =  1                              :        399907697
  j =  2                              :            46150
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.49e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.27e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.74
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   66.20
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.76
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.03
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.78
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.95
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5090.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12185.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.30
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999780230

Normal statistic for number of bits   :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.54
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999792299

Normal statistic for number of bits   :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.23
p-value of test                       :  2.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.94
p-value of test                       :    0.9984

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:27.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19005463.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.61
p-value of test                       :  1.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.48
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6829.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.52
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5215.07
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908218
  j =  2                              :            45885
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908058
  j =  2                              :            45959
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.02
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.67
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.46
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.85
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.81
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.98
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.00
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:23.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4704.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.60
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999983549

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.09
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999931835

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:43.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20086807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.65
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.39
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.01
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.66
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:58.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908520
  j =  2                              :            45737
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908059
  j =  2                              :            45969
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.75
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.11
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.20
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.91
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.16
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.63
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.61
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.55
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999904511

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.71
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999871214

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.27
p-value of test                       :    0.9995    *****

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:42.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 103  AutoCor, d=1, r=0               0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 98307.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.01
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.85
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.32
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.81
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907794
  j =  2                              :            46100
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46361
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870361
  j =  1                              :        399907278
  j =  2                              :            46361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17124.22
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.22
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.53
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.72
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.61
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.70
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.98
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.35
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.25
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000090022

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.05
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000116638

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.11
p-value of test                       :  9.4e-4    *****

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:43.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 103  AutoCor, d=1, r=0               9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1966083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1246
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334366
  j =  1                              :        599997508
  j =  2                              :             1246
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.97
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908722
  j =  2                              :            45633
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908143
  j =  2                              :            45927
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.66e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17249.07
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.28
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.40
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.59
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.67
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.53
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000071722

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.61
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999988055

Normal statistic for number of bits   :  -0.094
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:03.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2949123.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4204
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:17.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:12.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.73
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:50.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:28.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.72
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907895
  j =  2                              :            46048
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908514
  j =  2                              :            45737
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17068.99
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.99
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   55.44
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5180.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.95
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.21
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999992771

Normal statistic for number of bits   :  -0.057
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.09
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999923618

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:49.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      4.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3964943.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    3.01
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:53.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.74
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.33
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.26
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908398
  j =  2                              :            45795
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908625
  j =  2                              :            45680
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:12.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.06e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.13
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17596.56
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.57
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.66
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.35
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -401.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.01
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.77
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000026029

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.77
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999907130

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5046287.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1253
p-value of test                       :    0.9988

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334373
  j =  1                              :        599997494
  j =  2                              :             1253
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9946


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:49.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.53
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908686
  j =  2                              :            45657
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907796
  j =  2                              :            46099
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17772.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.58
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.79
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.11
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  272.14
p-value of test                       :  5.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.55
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.51
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.57
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.04
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:38.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5127.34
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.38
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.92
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999859361

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.50
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000115513

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:54.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    5.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6062095.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:48.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.24
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.33
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.25
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4763.65
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908062
  j =  2                              :            45966
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908477
  j =  2                              :            45760
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    7.32
p-value of test                       :  2.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  1.3e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.63
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.11
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.40
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.89
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  259.69
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.88
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.81
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.01
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.02
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.30
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000068905

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000006748

Normal statistic for number of bits   :   0.053
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.54

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft, t = 16                  1.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7077903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     655
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:49.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.54
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.94
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5258.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908696
  j =  2                              :            45646
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45348
p-value of test                       :    0.9935


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869348
  j =  1                              :        399909308
  j =  2                              :            45340
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17768.40
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.10
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.09
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.14
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.10
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.88
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.06
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.02
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.92
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.84e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9749.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.44
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.25
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000005221

Normal statistic for number of bits   :   0.041
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999945533

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8060943.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.74
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:51.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1602.71
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.00
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908089
  j =  2                              :            45951
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908727
  j =  2                              :            45635
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  7.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.09
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.31
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.03
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.49
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.76
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.54
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.57
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.02
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999988811

Normal statistic for number of bits   :  -0.088
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.96
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000006037

Normal statistic for number of bits   :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.83
p-value of test                       :  2.3e-3

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :  2.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9076751.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5614
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.07
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.03
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908477
  j =  2                              :            45754
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907745
  j =  2                              :            46120
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.23e-5
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.02
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.20
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.85
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.55
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.07
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.82
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.32
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:32.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   89.73
p-value of test                       :  1.6e-3


-----------------------------------------------
Total number of bits:  7999959735

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.73
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000083752

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:49.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10092559.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5280
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9977

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    3.20
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.61
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5195.61
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908375
  j =  2                              :            45808
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908076
  j =  2                              :            45956
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.56e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.50
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.29
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.05
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.68
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.69
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.02
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.50
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10291.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.37
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11434.34
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.20
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999950177

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.03
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000166969

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:20.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11042831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    3.90
p-value of test                       :  9.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.93
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5215.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908622
  j =  2                              :            45680
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908456
  j =  2                              :            45769
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17742.29
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.18
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.79
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.01
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.13
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.37
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999936470

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.16
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000128368

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:34.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12058639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7091
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.93
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.98
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908483
  j =  2                              :            45751
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908726
  j =  2                              :            45628
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.52e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   36.58
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.43
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.99
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.72
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.73
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.44
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.98
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.81
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.28
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.99
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.54
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999996533

Normal statistic for number of bits   :  -0.027
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.90
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999970274

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:01.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13008911.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.07
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908620
  j =  2                              :            45687
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908057
  j =  2                              :            45967
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.81
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.33
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.65
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.83
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.10
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.09
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.78
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000017062

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.08
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999970292

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.041
p-value of test                       :    0.48

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:36.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14024719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1214
p-value of test                       : 1 -  1.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334334
  j =  1                              :        599997572
  j =  2                              :             1214
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.35
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.53
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.05
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908524
  j =  2                              :            45726
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908405
  j =  2                              :            45796
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.97
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.65
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.35
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.03
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.91
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.75
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.83
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.35
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.59
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.84
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.79
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.89
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.06
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.54
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000062689

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.80
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000029254

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:42.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  1.8e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15040527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7548
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.73
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6779.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.50
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4816.41
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45567
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869567
  j =  1                              :        399908867
  j =  2                              :            45565
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908162
  j =  2                              :            45916
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  5.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.20
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.91
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.67
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.48
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.46
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.21
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5236.32
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.22
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.87
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.55
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.21
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:30.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12145.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000039586

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.51
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999943139

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.053
p-value of test                       :    0.52

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:42.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16023567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.95
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.93
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45546
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869546
  j =  1                              :        399908914
  j =  2                              :            45534
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907700
  j =  2                              :            46147
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17618.44
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.72
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.82
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.12
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.38
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.15
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.64
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5063.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.14
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999836138

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.20
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999935096

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.20
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:55.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17039375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7549
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:28.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:57.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    4.49
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:28.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.57
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.83
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908487
  j =  2                              :            45752
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17779.21
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.19
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.86
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.18
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.87
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.27
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.86
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5092.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.43
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000037849

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.93
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999817835

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:31.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18120724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:50.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.22
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.18
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908347
  j =  2                              :            45822
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908051
  j =  2                              :            45964
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17659.86
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.24
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.82
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.32
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.58
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.34
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.86
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.85e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.46
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.50
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999868544

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.16
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999928127

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:15.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19234836.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.31
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.54
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.68
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908627
  j =  2                              :            45679
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908505
  j =  2                              :            45740
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.04e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.39
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.20
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.31
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.16
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4816.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.02
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.78
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000118738

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.04
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  8000136279

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:30.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20250644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     973
p-value of test                       :  8.4e-3

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.59
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908738
  j =  2                              :            45628
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907774
  j =  2                              :            46110
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:19.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.30
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.27
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.20
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.17
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.21
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.05
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.77
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:31.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.20
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.59
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000001834

Normal statistic for number of bits   :   0.014
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.20
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000064936

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:17.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 131076.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.07
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.20
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908249
  j =  2                              :            45871
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45425
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869425
  j =  1                              :        399909157
  j =  2                              :            45411
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.37
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.68
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.58
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.01
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:31.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.66
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999967814

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.57
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999898340

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:08.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1245188.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4532
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7577
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6864.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907821
  j =  2                              :            46082
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908186
  j =  2                              :            45901
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -7.43e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17648.58
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.65
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.32
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.61
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.47
p-value of test                       :  4.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.92
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  486.23
p-value of test                       :  1.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.61
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.42
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.03

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.41
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.80
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:31.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000000511

Normal statistic for number of bits   : 4.04e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.43
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999966059

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    2.59
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   1.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2654232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:31.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908666
  j =  2                              :            45664
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908666
  j =  2                              :            45667
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:27.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17717.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.58
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.29
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.75
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.33
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.23
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.16
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.68
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.74
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999905729

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.72
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999986468

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:01.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3506200.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.53
p-value of test                       :  4.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1591.14
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.06
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907940
  j =  2                              :            46021
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46256
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870256
  j =  1                              :        399907491
  j =  2                              :            46250
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.29
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.78
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.79
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.20
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.03
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.86
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.73
p-value of test                       :  3.2e-3

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.62
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999996593

Normal statistic for number of bits   :  -0.027
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.29
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000154678

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.68
p-value of test                       :    0.9963

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:26.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4259864.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.52
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.06
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908611
  j =  2                              :            45690
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908239
  j =  2                              :            45873
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.15
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.53
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.30
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.97
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.29
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.42
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.76
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.69
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.98
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.55
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.65
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000107413

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000036160

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:56.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5242904.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    3.93
p-value of test                       :  9.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     998
p-value of test                       :  6.9e-4    *****

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.52
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:48.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908283
  j =  2                              :            45854
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907902
  j =  2                              :            46037
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.88
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.54
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.44
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.82
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.44
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.70
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.33
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.62
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000123958

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.16
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000019651

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:43.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        6.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6258712.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7053
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.12
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.45
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.19
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908547
  j =  2                              :            45719
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908026
  j =  2                              :            45981
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.56
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17792.38
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.27
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.50
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.94
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.58
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.66
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.04
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.08
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.12
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.80
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.56
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.61
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999913985

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.49
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000110353

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.048
p-value of test                       :    0.48

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8         0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7241752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.24
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.38
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4799.66
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907802
  j =  2                              :            46090
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908257
  j =  2                              :            45870
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.80
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.20
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.68
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.54
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.81
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.42
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.47
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.68
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.20
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.76
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.20
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.46
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.02
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.73
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000001975

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.98
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000014371

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:43.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8257560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.17
p-value of test                       :  7.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.86
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.21
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.32
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:59.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907845
  j =  2                              :            46076
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908045
  j =  2                              :            45976
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9912


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.99
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.38
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.83
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.81
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.90
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.02
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.26
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999910979

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.00
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999832325

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9273368.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5275
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:47.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.01
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.79
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908283
  j =  2                              :            45848
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907823
  j =  2                              :            46087
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.77
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.43
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.42
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.53
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.23
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.61
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.03
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.95
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999759095

Normal statistic for number of bits   :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.86
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999994160

Normal statistic for number of bits   :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10289176.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:36.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    4.45
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.21
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.36
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5235.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907752
  j =  2                              :            46118
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46215
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870215
  j =  1                              :        399907572
  j =  2                              :            46211
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17213.95
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.17
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.84
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.10
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4788.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.17
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.42
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.44
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.92
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.25
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000039256

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.67
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000144814

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:47.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11304984.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9965

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.66
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.55
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45412
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869412
  j =  1                              :        399909178
  j =  2                              :            45408
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399909000
  j =  2                              :            45491
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    : 1.70e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    5.90
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.56
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.59
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.42
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.89
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.57
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.60
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.66
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.30
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  258.52
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4326.16
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999978767

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.86
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000034114

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:42.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12320792.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    4.45
p-value of test                       :  5.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7262.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.04
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.05
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.33
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908798
  j =  2                              :            45598
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908080
  j =  2                              :            45957
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.79
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.25
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.31
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.80
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  479.10
p-value of test                       :  6.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.91
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.55
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.52
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.61
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.92
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:25.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.53
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000017476

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.32
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999969104

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:59.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   6.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13336600.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:35.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.50
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1293.19
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.55
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908507
  j =  2                              :            45739
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908134
  j =  2                              :            45927
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:18.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:19.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.4e-4    *****

Anderson-Darling statistic = A2       :    6.42
p-value of test                       :  6.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  186.69
p-value of test                       :  8.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.13
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.69
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.25
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.24
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.55
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  475.98
p-value of test                       :  9.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.03
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.91
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.72
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.45
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.05
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:24.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.83
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000031612

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.63
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999995522

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    2.73
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9901

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:44.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          8.3e-4
 78  RandomWalk1 M (L=10000, r=0)    9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14352408.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:36.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.73
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    4.21
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  176.25
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:20.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.93
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908508
  j =  2                              :            45740
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908618
  j =  2                              :            45685
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:18.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.24
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  174.58
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.60
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.49
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.28
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.59
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.87
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:22.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.51
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999917699

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999956624

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:23.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15368216.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    4.55
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   98.00
p-value of test                       :  2.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.90
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:52.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46197
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870197
  j =  1                              :        399907608
  j =  2                              :            46193
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:19.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -3.03
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:29.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:29.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   14.68
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17927.70
p-value of test                       :  4.1e-3



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.15
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.44
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.32
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.63
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.79
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.61
p-value of test                       :    0.9907

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:24.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.09
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999812738

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.68
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000063268

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:16.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         2.3e-4
 70  MatrixRank, L=5000              6.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16384024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5547
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.80
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.07
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.45
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.14
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908335
  j =  2                              :            45825
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45494
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869494
  j =  1                              :        399909013
  j =  2                              :            45492
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:18.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:12.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:28.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.03
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.85
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.89
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.18
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.09
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5259.61
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.80
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.39
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.78
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.40
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.25
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999837266

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.87
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999981224

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.22
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:27.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17399832.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  369.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.97
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.69
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46407
p-value of test                       :  7.0e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870407
  j =  1                              :        399907192
  j =  2                              :            46395
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908120
  j =  2                              :            45937
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.60e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:29.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   73.71
p-value of test                       :  9.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.24
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.82
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.65
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.82
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.11
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.94
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.99
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.46
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.28
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.76
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999975203

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.39
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000050197

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:04.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           9.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18415640.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:33.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.41
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908757
  j =  2                              :            45617
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46206
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870206
  j =  1                              :        399907593
  j =  2                              :            46196
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:29.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:29.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.97
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.49
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.86
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.94
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.89
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999906848

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.56
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000075808

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Tests on the sum of all N observations
Standardized normal statistic         :   0.083
p-value of test                       :    0.47

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:04.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19431448.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9948


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    8.74
p-value of test                       :  5.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1526.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.73
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5305.61
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45464
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869464
  j =  1                              :        399909073
  j =  2                              :            45462
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907823
  j =  2                              :            46084
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:29.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.09
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.23
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.86
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.65
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.96
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.32
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.22
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.96
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.11
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.18e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.43
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999996614

Normal statistic for number of bits   :  -0.027
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999851456

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:14.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         5.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 163845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5283
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.96
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.79
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    4.80
p-value of test                       :  3.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.57
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5182.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907949
  j =  2                              :            46024
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907935
  j =  2                              :            46028
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9904


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   55.10
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.49
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.26
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.85
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.16
p-value of test                       :  4.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.32
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.11
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.30
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.95
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.65e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.73
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999850475

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.01
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000046501

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:45.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1867781.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.45
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.68
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.86
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:59.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46317
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870317
  j =  1                              :        399907370
  j =  2                              :            46309
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908601
  j =  2                              :            45695
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.29
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17090.30
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.12
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.88
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.41
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.22
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.03
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:31.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.38
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000123793

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000038902

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2752517.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.94
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.85
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.51
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4814.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45430
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869430
  j =  1                              :        399909141
  j =  2                              :            45428
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908244
  j =  2                              :            45869
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.66e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.49
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.90
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.72
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4804.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.53
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.69
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.11
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.38
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.24
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999911939

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.91
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000259207

Normal statistic for number of bits   :    2.05
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:00.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3670021.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.76
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.02
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.84
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908176
  j =  2                              :            45906
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907830
  j =  2                              :            46076
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.24
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.35
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.96
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.86
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.00
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.04
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.84
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.91
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.51e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.85
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4347.81
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12021.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.85
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999907823

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.47
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999999497

Normal statistic for number of bits   : -3.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:06.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4751365.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.39
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908085
  j =  2                              :            45956
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908892
  j =  2                              :            45551
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.33
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.84
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.12
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.64
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.25
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.26
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.86
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  466.86
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.10
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.25
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.82
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    5.45
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.22
p-value of test                       :    0.9994    *****

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12048.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.92
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000127849

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.33
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999930446

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.22
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:56.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 83  LempelZiv, r = 15               0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5767173.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:40.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.58
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.77
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.25
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908005
  j =  2                              :            45996
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17753.85
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.34
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.79
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.34
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.42e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9762.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.57
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000006226

Normal statistic for number of bits   :   0.049
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.57
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999962960

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.36e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:19.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6717445.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:09.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.44
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7185.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.19
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907905
  j =  2                              :            46046
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908428
  j =  2                              :            45780
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  188.55
p-value of test                       :  6.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.89
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.75
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.66
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.31
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.90
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.41
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.24
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.21
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.23
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.72
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000013279

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.11
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000063550

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                0.9996 
 72  Savir2                          6.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7766024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.56
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.70
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908345
  j =  2                              :            45823
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.52
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.91
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.97
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.00
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.95
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4759.57
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.99
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.26
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.91
p-value of test                       :    0.9962


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.06
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:32.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11604.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.27
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000023101

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.31
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000083200

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:43.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8749064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1599.73
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.29
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:00.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908214
  j =  2                              :            45893
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46310
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870310
  j =  1                              :        399907382
  j =  2                              :            46306
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.60e-6
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17780.48
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.77
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.21
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  185.21
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4804.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.52
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.76
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.28
p-value of test                       :    0.9932


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:31.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3781.65
p-value of test                       : 1 -  7.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.26
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000128683

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.26
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000111151

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:43.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 97  HammingIndep, L=300, r=0       1 -  7.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9699336.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    3.32
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9916

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908447
  j =  2                              :            45775
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907925
  j =  2                              :            46030
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.13
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.3e-4    *****

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  181.68
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.92
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.23
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.38
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.26
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.14
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.46
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.39
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.25
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.40
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.50
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:34.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.65
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999886517

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.74
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000017362

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         : 1.00e-2
p-value of test                       :    0.50

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:38.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10616836.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.05
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.27
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.42
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908599
  j =  2                              :            45696
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907787
  j =  2                              :            46102
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.94e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17006.25
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.42
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.96
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.12
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.41
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.97
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.32
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.52
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.17
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.75
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9636.00
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:34.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.63
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999963959

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.00
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999928268

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.20
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:06.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11567108.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.77
p-value of test                       :  1.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.58
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7213.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.81
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:05.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908662
  j =  2                              :            45663
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908003
  j =  2                              :            45994
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.28
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.24
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.05
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.31
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.27
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.95
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.15
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.76
p-value of test                       :    0.9994    *****

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5096.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.82
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.64
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999986000

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.89
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000006391

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    2.96
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:15.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12681220.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6809.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.29
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908663
  j =  2                              :            45667
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45407
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869407
  j =  1                              :        399909189
  j =  2                              :            45401
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17228.48
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.87
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.31
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    2.50
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.00
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.84
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999826949

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.23
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000020914

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:33.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13467652.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.79
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:08.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907737
  j =  2                              :            46130
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908643
  j =  2                              :            45674
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.50
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.26
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.77
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.56
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.21
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.17
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.68
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.32
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9743.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.15
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.27
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999945704

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.71
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000030595

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:06.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14712836.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.52
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.13
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.21
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5238.50
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:53.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908310
  j =  2                              :            45839
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46183
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870183
  j =  1                              :        399907639
  j =  2                              :            46173
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.94e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17508.54
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.80
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.57
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.42
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.90
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.49
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.10
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.87
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.21
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:29.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.00
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000073417

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.48
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000176809

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         : -6.80e-3
p-value of test                       :    0.50

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15794180.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4168
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.14
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7338.59
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.07
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.20
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907864
  j =  2                              :            46062
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908415
  j =  2                              :            45788
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17465.22
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.53
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.76
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.29
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.68
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.34
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.34
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.59
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.94
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.01
p-value of test                       :  6.7e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -403.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.56
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:29.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4652.92
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.58
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000023611

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.69
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999908996

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:54.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 81  LinearComp, r = 0               6.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16711684.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1246
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334366
  j =  1                              :        599997508
  j =  2                              :             1246
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:37.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.47
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908888
  j =  2                              :            45550
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907804
  j =  2                              :            46095
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.20e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:14.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.77
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.34
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.46
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.51
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.69
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.34
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.10
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.26
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.12
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.20
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10352.66
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:28.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.66
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999942140

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999968513

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:52.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17661956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.05
p-value of test                       :  8.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.68
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:57.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908448
  j =  2                              :            45776
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908379
  j =  2                              :            45809
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17825.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.88
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.13
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.53
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.82
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.44
p-value of test                       :  6.7e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.49
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:29.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.91
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000059362

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.01
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000034858

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:25.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18743300.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5208
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    3.46
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.98
p-value of test                       :  1.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7191.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.44
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.85
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908539
  j =  2                              :            45723
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908213
  j =  2                              :            45886
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.46
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17601.30
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.34
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.52
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.24
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.00
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.18
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.28
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.53
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    2.49
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9772.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:22.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.78
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000068143

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.82
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999997853

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:49.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19660804.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.47
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.72
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.23
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908410
  j =  2                              :            45792
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908010
  j =  2                              :            45992
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.50
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.79
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.31
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.68
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.14
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.57
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5218.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.75
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.94
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:30.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.99
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999927299

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000002986

Normal statistic for number of bits   :   0.024
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:18.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 196614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    4.10
p-value of test                       :  7.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     997
p-value of test                       :  7.7e-4    *****

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.10
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:36.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.18
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908126
  j =  2                              :            45931
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908507
  j =  2                              :            45739
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:28.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17183.64
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.21
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.25
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.32
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -6.72e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:31.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.51
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.62
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999874520

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999974078

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.089
p-value of test                       :    0.54

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:09.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        7.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1277958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6733.84
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.86
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.56
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908940
  j =  2                              :            45524
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907667
  j =  2                              :            46153
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17065.89
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.20
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.82
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.82
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.88
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.79
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -401.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.32
p-value of test                       :    0.9953

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:31.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.76
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000063460

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.73
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999957575

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:40.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2686982.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.48
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908420
  j =  2                              :            45784
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908027
  j =  2                              :            45982
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.35e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17177.93
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.84
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.76
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.59
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.36
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.52
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.00
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.97
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000029656

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.28
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999978125

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.026
p-value of test                       :    0.49

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3571725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9953

Test on the Nm values of W_{n,i}(mNP1):    4.41
p-value of test                       :  5.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     351
p-value of test                       :  2.2e-3

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.51
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.48
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.69
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908636
  j =  2                              :            45676
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907705
  j =  2                              :            46146
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9945


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.43
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.78
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.91
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.71
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.14
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.23
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.52
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:31.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.49
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999924389

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.55
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000095332

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    2.41
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:26.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4521997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908752
  j =  2                              :            45621
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908555
  j =  2                              :            45712
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.35
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.12
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.06
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.54
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.81
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.23
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -401.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3845.31
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.38
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999980327

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.65
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999951371

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:06.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5341197.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.28
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.72
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45481
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869481
  j =  1                              :        399909041
  j =  2                              :            45475
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908401
  j =  2                              :            45795
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.16e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 6.26e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.27
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.25
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.21
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.54
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.79
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:31.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.06
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000006310

Normal statistic for number of bits   :   0.050
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.82
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000009262

Normal statistic for number of bits   :   0.073
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.84

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:27.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6488078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    4.06
p-value of test                       :  8.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     343
p-value of test                       :  8.0e-3

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:35.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.51
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4813.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907857
  j =  2                              :            46061
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908090
  j =  2                              :            45946
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.30
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.56
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.94
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.75
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.39
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.05
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.50
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.27
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.37
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:31.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11604.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.82
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000154969

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.83
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000030658

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:47.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7340046.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.81
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908268
  j =  2                              :            45863
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908698
  j =  2                              :            45645
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  6.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.90
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:28.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17085.48
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.13
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.83
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.21
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5213.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.78
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.16
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -401.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.86
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10286.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5222.51
p-value of test                       :  4.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.70
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999806771

Normal statistic for number of bits   :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999930686

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:24.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 95  HammingIndep, L=30, r=0         4.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8323086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.44
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908369
  j =  2                              :            45811
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907986
  j =  2                              :            46004
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.64
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.18
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.16
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.12
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.48
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.22
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.53
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -401.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.41
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5130.99
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3905.86
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.90
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999939590

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.33
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000013060

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:56.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9568270.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:37.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1312.98
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6721.61
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.40
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:52.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908244
  j =  2                              :            45869
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908316
  j =  2                              :            45830
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.50
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.00
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.49
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.98
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.49
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.84
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.69
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3922.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3886.01
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12141.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.43
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999950540

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.98
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000059137

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    2.82
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:24.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10485774.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:26.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:29.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:45.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    4.00
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    3.30
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.19
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.14
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.63
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5330.25
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907932
  j =  2                              :            46028
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908155
  j =  2                              :            45915
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9940


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.03
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.95
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.39
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.29
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.45
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.54
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.41
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -401.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11514.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.68
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000138238

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.74
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999978941

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:38.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 40  Permutation, t = 3              0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11632668.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:46.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9908

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:16.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:51.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.15
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.27
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908985
  j =  2                              :            45506
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908832
  j =  2                              :            45584
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.06
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.36
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.05
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.13
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.82
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.34
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:28.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000017686

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.61
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000020035

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:40.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13172764.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:20.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:50.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.31
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45311
p-value of test                       :    0.9961


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869311
  j =  1                              :        399909383
  j =  2                              :            45301
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907772
  j =  2                              :            46108
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17114.38
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.01
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.75
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4757.63
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.40
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.77
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.99
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.92
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.11
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.07
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.36
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000052288

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.24
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000150793

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:50.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14188572.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.67
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    4.02
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:50.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.94
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.49
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908553
  j =  2                              :            45719
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908028
  j =  2                              :            45983
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.21
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.28
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.79
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.28
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   42.59
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.87
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.06
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.62
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.36
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.17
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.20
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.02
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:29.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.30
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000216379

Normal statistic for number of bits   :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.20
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000000859

Normal statistic for number of bits   : 6.79e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.21
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:40.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15204380.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:48.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.73
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908678
  j =  2                              :            45658
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908398
  j =  2                              :            45789
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.84
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.55
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.65
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.55
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5184.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.95
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.54
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.42
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.00
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:30.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12217.41
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.06
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999980396

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.07
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999834611

Normal statistic for number of bits   :   -1.31
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    2.62
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:35.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16220188.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:53.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  350.58
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6861.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.25
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.72
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907821
  j =  2                              :            46085
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45422
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869422
  j =  1                              :        399909160
  j =  2                              :            45414
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9904


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:29.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.65
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.37
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.40
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.65
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.79
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.20
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.39
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.31
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.08
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.78
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:09.87

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.93
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999932354

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.00
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000067006

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:39.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17235996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:48.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.84
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46146
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870146
  j =  1                              :        399907711
  j =  2                              :            46140
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907994
  j =  2                              :            46000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  111.11
p-value of test                       :  5.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:29.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17261.38
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.06
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.66
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.43
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.19
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.45
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.07
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.03
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.48
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.12e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:30.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.98
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000082180

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.96
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000030310

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:18.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            5.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18251804.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9930

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:50.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1559.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.63
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908114
  j =  2                              :            45940
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46290
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870290
  j =  1                              :        399907424
  j =  2                              :            46282
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.53
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.30
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.30
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.25
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.98
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.08
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.01
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.64
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.47
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999984548

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.04
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000173545

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    2.42
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:14.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19202076.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n86, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.38
p-value of test                       :  6.8e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     262
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.35
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908299
  j =  2                              :            45846
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n86, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908414
  j =  2                              :            45790
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:09.57

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-6
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.55e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17198.61
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.06
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.52
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.91
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.09
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.69
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.07
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.52
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000032380

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.82
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999965519

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n86, Linux

MT19937


sstring_AutoCor test:
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   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


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Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.59
p-value of test                       :    0.80

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CPU time used                    :  00:00:58.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:08.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP, t = 5           6.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




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